The nearby world (let's say, the state of Texas) looks to be like its former self but post-apocalyptic. While there are no signs of nuclear explosion (and no toxic radiation to deal with), the place looks as if there had been one. The places are generally desolated with little population (if there are any "innocent" civilians, they would be hiding). There are cars but for some reason you don't see them being used (perhaps they would stand out too much? Fuel's not a commodity anymore?). There's little electricity, and only in some places with fuel generated machines. Every useful store (pharmacy, supermarket, minimarkets) has probably been ransacked by raiders. The world "far away" (other states) you don't know. But hey, your character is always welcome to explore the "map".

As to the specific location... sorry, I must admit I don't know much about Texas to really tell. In my head, it's like New York City but smaller, and with less skyscrapers.

I hope this helps. If not, let me know. I don't mind questions at all.