Vacation in Brazil-please advice (Rio de Janeiro)

Hi Everybody! Iam going with my boyfriend for a holiday to Brazil in beginning of March. I wonder if anybody can advise where to go. We have 9 nights and want to see Rio for 2 days and then go to a beach with not so many tourists. I read about the island Ilya Grande not far from Rio. Is it nice? Anybody can recomend me where to stay there. We want a room at the beach and it should not costs more than 80 Euros per night. And how is the weather in March?
Thanks a lot!
Katarina