Where should I go for my next duty station?

I would strongly vote Germany. You are already familiar with Stryker's so why not go shine there? Also, you and your family get paid to live in Europe. Your family will love the experience.

If you're not familiar with a base, I would suggest you visit the Military Installation page* on Military One Source. This will at least get you started with the demographics information, key population centers around it, a little bit of history and a number of "you should know this if you are being stationed here" items.

Another place that has good information is Millie*. Note: this is geared towards hooking you up with real estate agent, but it has a lot of great information about the posts for you and your family as well as allowing you to connect up with "scout" who are military spouses who's significant other works at the base (kind of a "contact-an-informal-sponsor" type thing).
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* https://installations.militaryonesource.mil/
* https://www.gomillie.com/

SSG (Join to see)
Fort Campbell would be a great choice in my opinion. It's close to Nashville, and Clarksville is a fairly good size place. Hopkinsville (KY) is also close but not as much to offer as Clarksville. Had basic and AIT at Polk in 1969, and the only place close by was Leesville aka Disease Villegas! Probably a lot has changed since then. You didn't mention Knox, and my memories of it (and Jackson) are nothing to be excited about... okay, I guess.

Places I have been stationed on your list and how I would rank them: Germany, Bliss, Hood, and Korea. Bliss comes out ahead of Hawaii and is a hidden gem. It has a ton of outdoor options to include playing on BLM land and heading to the mountains 1.5hours north. Grew up in KS near Riley and did NG rotations there as a teen. I would have done Riley if given the chance. Lewis is beautiful and reminds me of Germany. All the craft beer there really makes me think of Belgium. Attached to the 10th in Afghanistan and could not stand them. I started life as a 91B medic in an engineer bn and have more than a few nights sleeping under the stars in Central America. Stateside Bliss has been the best location for my family and I. Huge youth wrestling there and so much for your children to do. Get the wife involved with family support groups, gives her a great social outlet and being senior in my unit (SR rated by brigade level) I often found her knowing as many or more of the senior folk than I did. Made the social events so much more enjoyable for both. My wife was on a first name basis with two of my O-6 raters' wifes.

Spent a night at Hood visiting friends on a cross country trip. Have literally never heard a single good thing about it, and my night there did not change that outlook. I can't really claim full knowledge, though.

My knowledge of Polk comes from multiple JRTC rotations. Not a huge fan of the environment there, but I am sure things are different for permanent party, so not a lot of help there, either.

I did 3 years in Germany, and it was awesome. But they have changed pretty much everything since I was there, so I have no idea what to tell you. I still hear good things, and Bavaria is guaranteed to still be beautiful if you get stationed down there or can visit. Plus, travel throughout Europe is nice. Get your passport now!

I spen a week at Bliss on two separate occasions. Meh. Not good, not bad. Ups and downs. Of course, I obviously did not have the full Bliss experience. But there are definitely worse places to be.

Bragg... oof. They are their own world. You will love it or hate it. I was only there for a few days for a competition. I hated it. But I hear a ton of folks who can't wait to get back.

I can tell you next to nothing about Riley, Korea, JBLM, Stewart, MacDill, or Myers. Which leaves....

Drum. It is flipping COLD. Like trees EXPLODE cold. Like, "I'm sorry, it is too cold to run a truck, you have to stay in the field an extra 24 hours" cold. It is also more or less in the middle of nowhere. Which is a blessing and a curse. If you like outdoorsy stuff - hunting, hiking, fishing, skiing, etc. - you'll love it. If you like high society culture - museums, theater, music, etc. - or even grunt culture - strip clubs, bars, and gun shows - you'll hate it. NYC is 6-7 hours away, so you CAN get to the high society stuff, but it is tough. Syracuse is a little over an hour to the south, and Kingston is a little over an hour to the north - in Canada. Both can feed your grunt culture, but driving back an hour to an hour an a half after a night on the town ain't fun. And is expensive as hell for an Uber. Drum, more than any other place I have been is a "what you make of it" post. It has the potential to be the best place you have ever been or the worst. AND.....

Campbell. I literally have nothing bad to say about the place. Clarksville is a great town - and growing (which MAY be a bad thing if you don't like cities). Nashville is an hour away and has a surprising variety of entertainment - from clubs, to museums, to sports (NHL, NFL, MLS, minor league baseball, and an SEC school), to the music scene, and more. And some seriously good eats, too. Campbell's support staff (finance, MWR, DEERS, AAFES, even CIF) treat the Soldiers (and families) like VALUED CUSTOMERS instead of the normal treatment like you are interrupting their more important work. They have a large veteran community - and growing (myself included) because the surrounding area has embraced them. Great place to live, great place to work, great place to retire. I was planning on retiring near Knox - own a home there and everything. Then I got stationed here and, well......


Hope that is at least mildly helpful.

I don't know a lot of your career goals or what skills you have (airborne, air assault, ranger etc), but with that:
Honestly, Germany was a dream for travel, but if you don't intend to travel around, probably not worth dragging everyone out there for 3 years.
If you're focused on training and progressing, 10th Mtn at drum is great for that; they also have a great pre-ranger program if that's on your list. Plus adds light infantry time to your experience. There is still plenty to do up there, despite what people say. Canada is 30 minutes away, and Syracuse is 1.5 hours.
I enjoyed Korea, but again travel. I also feel like your career would stagnate a bit unless you took on civilian education, no real military schooling out there.
Bragg would get you some airborne time, always looks great on the ERB plus jump master will boost you moving forward as well. Also a good pre-ranger program.

Those are the ones I have personal experience with, and the best I can give you for a short list of things to think about.

Wow my friend you put down alotvof options. I recommend you follow the Col thought and visit the homepages for each. Narrow a bit in your own, check schools kids programs, daycare etc.

I am biased Germany isba Gem, but also has its drawbacks. Great travel and vacationing, great schools, Stryker is happening and a riatation/deployment to Poland or other is likely. Training is full spectrum, not only roll out the gate for training, but including all aspects of vehicle/equipment prep. Raul planning and management all while training for a rotation. Graf is out the gate from the MP and HTA is a rail away.

There are literally hundreds of sites and activities within hours drive making for awesom family weekends and Vacas.

The food, the culture, the beauty of it all. You can stay in the Alls at a military rate and enjoy summer and winter fun.

Anyway, do sone more homework.

I liked Germany, Warner Barracks, Bamberg, but I haven't been there since the early 90's. The only downside to Ft. Campbell is that the 101st deployment schedule used to be very busy, so you spent a lot of time other places. Haven't followed their recent activities. Oh, and a lot of the base facilities are relatively new, a lot of it built since 2001.
Riley is out in the middle of nowhere. Nothing bad about the base, but nothing thrilled me about it either.
Warner Barracks closed, but I would still recommend Europe.

My Son Was Stationed At Hunter Airfield Which Is Part Of Ft Steward Command And I Lived In The Area For About 2 Years, There Are A lot Of Recreation Activities Around The Area You Have Fresh And Salt Water All Around If You Like Fishing And Boating, There Are Beaches Close By, Lots Of Hunting Areas Around, Great Southern Food And Housing Off Post Is Not That Expensive , Plus It’s Not That Far Of A Drive To Florida For All The Recreational Activities There ,
My Son Loved It So Much When He Retired He Stayed In The Savannah Area.
Ft Bliss Is On The Border In The Middle Of Desert I Was Stationed At Bliss For 2 Months For Advanced Driver Training And Couldn’t Wait To Get Back To Ft Irwin , Go Figure But It Was That Bad, My Wife’s Cousin Lives In El Paso And Is Selling Their House Because It Has Gotten So Bad In The Current Environment There With All The Illegal’s Streaming Across The Border, The Crime Rate Has Soared And Car Theft And Burglaries Increased Tremendously In The Past 2 Years, Plus Not A Whole Lot To Do With Families In The Area.
At Ft Irwin You Are A Few Hours Drive From Vegas And The Beaches Around Los Angeles And Lots Of Family Recreational Activities In California.

Germany