Check out a guidebook, go to Expedia and see what's available. There are lots of non-chain hotels in Ipanema, Copacabana, etc that are perfectly fine and will cost somewhat less than the big chains.

I disagree somewhat with newyorkgeorge - English may not get you very far in Rio at all. You'll find that the expensive international hotels will generally have lots of English speakers on staff, but even a bit down the scale you'll be lucky to find a guy with an accent that sounds like Count Chocula with whom you're 50% able to have a coherent conversation. Do not at all expect shop clerks, waiters, taxi and bus drivers, people at drinks stands on the beach, etc. to speak English. Brazilians are not known for being multilingual.

Weirdly, Spanish is also very rarely spoken - Brazilians will all say they speak Spanish, when what they mean is they can't speak it at all but can more or less understand if you speak it.