What are some great posts to reenlist and ask for?

Anywhere in Germany!

Pretty much anything OCONUS. Japan, Korea, Europe, Hawaii, and Alaska can all be great assignments if you get out and see the world.
CONUS, I think JBLM, Carson, Eglin, Hunter AAF, Rucker and anything DC area are all good areas that people like.
As far as units the most common favorites that people tell me they want to go back to are: 82nd, 101, 3ID in Benning, SF Groups, 4/25 in Alaska, 25ID in Hawaii, 173rd, and 10th Mountain in Drum.

Ft eustis was fun and close to virgina beach Busch gardens colonial Williamamsberg, historical Jamestown not too far from D.C. Tons of stuff to do there my favorite duty station and plan to move back there someday

NOT Bragg because Black Hole, especially is Airborne
Korea for traveling, KDSM, OSR, and overall good stuff
Germany because I've rarely heard negative things about it from guys who went there and got outside the barracks
NOT Bragg because 82nd
Carson because recreation
Irwin if you want to hate your life and have Vegas ~2 hours away
NOT Bragg because blah
Japan because its a very difficult PCS move to get
And NOT Bragg because Bragg

GERMANY. Then, you could also ask for GERMANY.

Thanks to the Army, I've been to all the continents less Antarctica. I say reup for anywhere overseas. Just by posting this question, I surmise that you are not a barracks rat and therefore will thrive anywhere -- duty stations are what you make of them, so you might as well see the world on someone elses's dime.

SPC (Join to see) not sure there is anywhere in the world better than Fort Bragg. Center of the universe! ATW.

In all reality depends on what you want to do. Do you want to jump if so Bragg. If you want to do something special with your MOS or other skills there are other bases that might be better depending on what you want.

Pretty open ended. What are you interests? Family's interests (if applicable)? Where is your family and would you want to be near them again? How would a duty station shape or create your short and long term goals? How could you see a duty station effecting promotion potential or career longevity?
Nearly all duty stations will offer good and bad for the masses, the important thing is to figure out what each will offer for YOU?

Japan was awesome.

Used to like Ft Sam until the Air Force took over security

I'm kinda biased but for me it would be Hurlburt Field Fl. or RAF Mildenhall England both for AF Special Operations.

Korea, I came down on orders for Korea on my 19th year in the army. After some soul searching I decided to try to get command sponsored. It worked, I took my family to Korea and we spent 3 years in yongsan. It was a great experience, my entire family loved it there. We were a short hop away from Japan, where we spent a couple of weekends in Okinawa, and the culture was amazing. There was always something to do. I worked don't get me wrong but it felt like I was on vacation for 3 years. We have been back for 2.5 years, retired and my family wants to vacation there this summer.

Just remember there has to be a need for your MOS at the requested duty station or it will be denied. For example, if you were an Abrams Tank Crewmember (MOS 19K) you can only go where they have Abrams Armored units. Many other MOS' will have similar restrictions.

If you enjoy seeing new places in general and are not too particular about a specific post than just about any one would be worth it. All offer something to enjoy outside of work. Some more than others as you may have heard from fellow Soldiers with their experiences. Some notable ones you might want to consider are: Ft Carson, CO. Ft. Stewart, GA. JBLM (WA). Ft. Campbell, KY. Those were places I enjoyed especially at Ft. Stewart because we were close to the beaches and the area has a long rich history to explore all year around. It was my opportunity to travel with my family up and down the east coast to visit big cities and other places.

SPC (Join to see) Anywhere outside the USA

Do you want to be close to home? If you like being close or in a big town or city, Fort Hood, Fort Bragg, Fort Bliss, Fort Gordon, Fort Sam Houston.... depends on your preference of states... Hawaii?

Italy, Germany, and FL!

Bragg

I was stationed in Fort Stewart I would say this I am glad I'm out of that place. OCONUS are great, Fort Carson, and any AF Base that have your MOS like mine.

HAAF, Georgia... It was my favorite duty station throughout my entire career.