My class stayed at the Fairfield and there was a ton around there in walking distance. I do not regret not bringing my car-- but having said that, I am very greatful that others did because it was helpful. I paid the owner of the car each week for driving us around to class and back.
Here's the other thing, there really is no good gym close by so having a car would have been nice just for that if you have a membership somewhere like LA Fitness or others which are a few miles away.
You get your travel benefits on day 16 exactly, its US Airways policy that you have to be an employee for 16 days I believe. The company will positive space you anywhere you need to go -however- if you decide to leave training on the weekend you are on your own to get back in time. I left twice while staying in Dayton, on the third weekend and on the fifth I think. In both cases from Dayton to Charlotte and Charlotte to Dayton (those are psa flights) I had no choice but to ride in the jumpseat because the flights were full. And you are not in CASS at that point so there are some hoops to jump through to get the jumpseat which confuses the people in Charlotte for some reason.
Oh side note- absolutely take one of your weekends as see the Air Force museum, its incredible and free!