I'm 19 (close to 20) and have never been stopped checking into a hotel (with a published 21 check in age) on my own. I've been doing it since 1.5 years ago.
I second that as long as you have a valid credit card and valid ID, you should be fine. Dressing up should help. If you look much older, then you really shouldn't have a problem.
I've stayed in hotels (under my name) and have had the booze still in the minibar. Once I had a friend (also under 21) over who lifted one of the bottles to look at it, put it back, and the hotel wanted to charge me for it.