Hello Sara,
Neighbourhoods I recommend you to look for:
Ipanema
* Quite pricey as above
* Touristy
* The beach's crowded
* Considerably expensive.
* Only fancy bars stay open after midnight.
* Not really a interesting area in my opinion, totally overrated.
Leblon
* Exactly the same as Ipanema.
Copacabana
* The most visited neighbourhood by tourists.
* The beachfront sidewalk is pretty, but packed.
* Everything can be made by foot.
* Many metro stations in this area.
*Not too safe on late nights.
Botafogo
Quite local
* The best neighbourhood in my opinion.
* Close to everything.
* Close to city centre,
* It has a nightlife, bars stay open almost until morning.
* Very good street market.
Flamengo
* Nice neighbourhood
* Very close to the city centre
* Mostly residential
* Close to many other nice neighbourhoods.
Laranjeiras
*Same as Botafogo and Flamengo, but no metro station.
*Transportation here on late nights can be tricky.
Barra da Tijuca
* Jardim Ocenico area specifically
* Local
* Everything can be made by foot,
* Brand new metro station with the same name (Line 4)
* The beach is better than the ones in Ipanema, Copacabana, and Leblon.
* A little bit far from the city centre, but well served with transport.
*Safer than most of the areas in the south zone.
Urca
*This neighbourhood is loved by locals and tourists.
*Pretty calm and charming.
*Transport here is very difficult.
Santa Teresa
*Very charming area
*Filled with slopes, making it pretty tiring.
*Very touristy.
*It can be dangerous at night.
*Transport here leaves much to be desired.
*Some of the greatests views of the city.
I'd avoid Lapa, Catete, Glória, Tijuca, São Conrado, Recreio.