Is Camp Casey inside or beside Camp Carroll, and what is Camp Casey like?

Camp Casey isn't a bad assignment. You'll definitely learn your job, whatever that may be. Bus system is pretty decent and taxis are plentiful for on post transportation. Food options are fairly limited on post. Off post in the "Ville", or in Jiheng where I prefer, there is lots of great food to choose from. Good Korean BBQ is hard to beat. You'll be able to take advantage of lots of 4 day passes. Take the train to Seoul and experience the culture. Go on an MWR trip to the DMZ or go snowboarding at a resort. Being stationed in Korea you'll have affordable opportunities to see and do things you might never get the chance to see again. Just use your time wisely while you are here. There are good intramural sports options here, two pools, and a few nice gyms as well. There are ample opportunities for you to begin working on an Associate's Degree while you are here via the Education Center on post. Most importantly, and I can't possibly stress this enough, understand the rules associated with the curfew policy and follow them. Too many promising young soldiers don't take this seriously when they arrive, and they risk ruining their career before it even begins. Your unit will explain this further upon arrival. Take it seriously.

And when I google map the distance between Casey and Carroll....the distance was like a 5 hour and change train ride

For starters, Casey and Carroll are nowhere near each other. As for details of Camp Casey, try this link for starters:

https://www.thebalancecareers.com/installation-overview-camp-casey-korea-3344631