What are some things I should look into doing while assigned to Landstuhl? Is there a decent used car market near the base?

Well, don't become either a barracks rat (someone who never leaves the base) or an alcoholic. As to a car, you will probably get the best deal buying one from someone about to be reassigned. (Most bases have car adds in the post newspaper.) Also, don't blow all you money on a new, or used, Porsche. Wait until you are a captain.
As to what to do - get out an explore. There is a lot of beautiful scenery in and near Germany. I'm not familiar with Landstuhl but you should make a trip to Munich to visit the beer hall, go to Stutgaart and see both the Mercedes and Porsche museums, Nurnberg for the railroad museum an Heidelberg for the castle with the world's biggest wine flask. When you get a long weekend go to Paris, Vienna, Prague or Budapest - you will be glad you did.

Excellent shared info on Landsthul. You will have a fun time there and traveling all about. Great assignment!

There is a healthy lemon lot market all over Germany. LRMC is right next to Rammstein (literally across the autobahn from me another). You have Another kasserne just down the road. Baumholder is about 30 minutes away.
I bought a beater Opel for $500. I drove that until I decided to buy a Mini. You can go cheap or you can buy expensive. German spec or American Spec. PS you can't bring German Spec's.

I doubt there will be BOQs. You are looking at a apartment or house downrange on VHA.

Not sure how it works in Germany, but when I was in Korea, I bought a car from my predecessor. When I left, I sold the car to my replacement. He sold it to his replacement, who sold it to his replacement, who is about to PCS and, you guessed it, sell the car to his replacement.

Drive a lap on the Nurburgring.

Plenty of people have their trucks in Germany.

They did not have BOQ while I was there and doubt they do now. Lived in a beautiful place. They will ship your truck, what kind is it?

Also, in regards to the truck, what size truck are we talking about? And have you made any modifications as far as tires, exhaust, or suspension? In Germany, it is prohibited to have the tires protruding past the fender of the vehicle, and it cannot be excessively loud.

One thing to definitely be mindful of regarding Germany, and Europe in general, is that parking spaces and space in general is a short commodity. The parking spaces are a lot smaller and a good number of parking garages have low clearances and tight spaces for turning. My 2013 VW Passat went from being a midsize to full-size by European standards when it shipped from Ft Hood. And when it comes to parking on the streets, you'll need a lot of room. And the Germans will back in tight. I run into this often.

As far as parts, you'll be spending a lot of time ordering from online. Tires, there's a tire shop in Wiesbaden southwest of Clay Kaserne near Mainz that may be able accommodate you. Winter or all weather tires are a requirement by German law during winter. A general rule for when it required is O to O, Oktober to Ostern (October to Easter). There is a Troop Auto Hobby shop with bays on the opposite side of the airfield at Clay to do your own oil changes, tune ups, parts replacement, and repairs. There are some shops on the economy that might work on American autos, but you have to look for them and can get pricey. Plus you'd have to schedule well in advance.

Shipping your vehicle may take just under 60 days to get to your pickup point. So be prepared to be without your vehicle for a while if you ship it close to your departure time. Be sure to inform your sponsor of this.

Another thing-- if you like to ride a ten speed or such is great and you can have fun while exercising, we used to ride 20 miles for a good ice cream cone then back just for a Sunday afternoon.