Rather than taking a taxi, you can take a bus from the Rio de Janeiro international airport (GIG) to your hotel in Copacanana or Ipanema.
Executive Bus to/from GIG/SDU (‘ônibus executivo’ in Portuguese)
The air-conditioned buses from the Real Premium company provide the cheapest reasonably safe transportation to your hotel. The fare is R$12; US$6; €5 (cash, only in reais), and the trip takes about one hour (roughly an hour and a half during rush hour).
These buses do not take a direct route, stopping at the Rodoviária Novo Rio (bus terminal) and Santos Dumont Airport (SDU), passing through Flamengo, Botafogo, Copacabana, Ipanema, Leblon, São Conrado, and ending at Barra da Tijuca (you can get off either in front of or nearby your hotel in any of these districts).
Before entering the bus at Rio de Janeiro international airport, you must inform the driver/cashier operator of your destination, since there are two different routes. These buses operate from 5:30 a.m. to 11:30 p.m. daily, with departure from GIG every 30 minutes.
They can also be caught back to either airport (GIG or SDU) at the main beach avenues of Copacabana, Ipanema and Leblon (on the beach side) across from major hotels.
Browsing the Internet will not be enough to access all the relevant travel information pertinent to Rio de Janeiro. To learn all that matters get a PDF copy of the e-book My Rio Travel Guide – The Essential How-To Visitor’s Guide to Rio de Janeiro.