It's not a particularly charming area, but it is convenient and really not so bad as some will suggest. If you head two blocks northwest of Termini, to Republica, you're now in what's considered a desirable area to stay, with many high-end hotels. To the west a couple blocks is Monti, which is currently considered very desirable.

But if being next to the train station is going to bum you out, sure, pick another hotel. So many options in Rome, though prices have really gotten crazy for the good ones.
I would never recommend that a leisure traveler visiting Rome stay at the airport.