You'll probably never get the beach to yourself, even in the winter, but you'll have a lot more room to relax during the off-season. The rates for beach hotels are considerably higher than those for hotels just a few blocks away from the sand. Since bathing attire is perfectly acceptable in the street and on mass transportation, there's really no reason to pay more for a couple of blocks. Save your money for the arts and crafts market that lines Copacabana beach on the weekends. This may seem obvious to most people considering a trip to Rio, but do go to the beach.
People gather there to relax after work, to unwind on the weekends, and to meet with friends.
If you don't spend some time on the beach, you will not have seen Rio. Even the sun-sensitive can partake since most hotels will lend out giant beach umbrellas. In addition, the city is physically enormous, so you'll want to give yourself plenty of time to see as much of it as you can. The traffic in Rio is a nightmare, not only because of the volume of cars but also because certain main, absolutely necessary streets run only in one direction during rush hours. You will not be able to figure it out during an average vacation-length stay, so don't even try.