I don't know your definition of luxury but the nicest hotels are probably:

Copacabana Palace- the grande dame of Rio hotels and has a superb Italian restaurant Cipriani, a great pool and a delightful location. Surprise, it's in Copacabana.

JW Marriott- further in Copacabana, small, and quite nice for a Marriott. The Executive Lounge has great views and there's a wonderful rooftop pool.

Sofitel- at the end of Copacabana across from Copacabana Fort. It has a great French restaurant, Le Pre Catalan.

Fasano- a couple minutes walk from the Sofitel but just barely in Ipanema. It also has an eponymous restaurant. It is the most expensive and newest of the lot.

Just now those are the primary hotels considered to be luxurious in Rio between Copacabana and Ipanema. There are many, many more and also a number of wonderful boutique hotels, several of which are in Santa Teresa, a very colorful neighborhood that has a tram which is a tourist attraction of it's own. Santa teresa is quite far from the other areas but is very popular with people who know Rio quite well.

Rio is going through major efforts to clean up the crime, with good success, car thefts have dropped over 63% in the last week, for example. During March, if present trends continue you'll have much less crime than you've heard about.