"Not too expensive" is too subjective a criteria. Also the time you mention is still high season and prices in Rio have been going sky high in general recently.
Give us a price range, preferably in reais.

Hi There,
As I am traveling alone am looking for somewhere, safe, with a pool and central and max to pay would be 329 BRL.
Thanks for your help.

Jollydee

First of all, you'd ideally want to be staying in Copacabana, Arpoador, Ipanema or Leblon, all beach neighborhoods with many hotels just a block or so from the beach. Space for pools is at a premium in these neighborhoods, so the ones that exist are mostly rooftop and many are just smaller plunge pools.
Bear in mind that Rio is pretty compact when speaking about sights and hotels.
For a bit more than you mentioned, I'd recommend the Praia Ipanema for about R$380.
Hotels with pools (without regard to price) include Copacabana Palace, Mercure Apartments in Leblon, Porto Bay Internacional Rio (jacuzzi size "pool"), Sheraton Rio (a bit out of the way), Fasano, Windsor Atlantic, Ipanema Plaza....