To become familiar with city neighborhoods and things to do, take a look at the site www.ipanema.com for an informational overview. Four nights is barely enough time to get a small taste of this marvelous city though.
After you visit the most famous sites, the must-sees like Sugarloaf and the Christ, consider some of the lesser known things I enjoy in Rio:
* a ferry ride from Praca XV across the bay to Niteroi--great views back toward Rio. Visit the fish market for lunch and the Niemeyer designed art museum, perhaps a great local beach, or the city park for more views.
* a visit to the Feira Nordestina to get an idea of the culture, food and music of the northeast
* a night out dancing samba with the locals to a live band at Carioca da Gema in Lapa
* a night at one of the samba school's rehearsals or a feijoada lunch, at their home ground
* coffee and pastry, as a break from walking around downtown to see so e historic buildings, at the classic Confeitaria Colombo
* a meal at Aprazivel, while exploring the architecture, shops and small museum in Santa Teresa, and/or at Bar do Mineiro
* the beach at Joa, if you can find a taxi to get you there and come back for you
* one of the vista points! like Vista Chines, up in Tijuca Forrest
* the waterfall and the koi pond in Tijuca Forrest
* the small museum in Quinta de Bia Vista with some ethnic objects that are truly very fine art, set in a lovely park/zoo

Food:
Also look for Veja magazine's annual list of bests.
Cipriani in the Copa. Palace for Italian
Por kilo places for lunch, great variety with veg options
Arab or Amir restaurants, reflecting that large population
Marius seafood
Antiquarius for Portuguese
Roberta Sudbrack or Claude Troisgois' Olympe or Carame if you want to splash out
Palaphita Kitch for Amazonian inspired cuisine
Street food such as tapioca, a sweet or savory filled pancake
Tropical fruit juices
Fellini's buffet
Galeto de Leblon, feijoada lunch, but not really for vegetarians :-(
Siri Mole for Food from Bahia
That ought to keep you fed for 4 days, don't you think?