If you're looking for accommodation options in Havana, here are the main ares to choose from: Cerro, Habana Vieja, Old Havana, Plaza, Plaza de la Revolucio and Vedado Centro Habana. I personally would suggest stsying in the Prado, which is located between Habana Vieja (Old Havana) and Centro Habana (Central Havana). There are also plenty of Casa Particulares to choose from in these two areas.
You'll find the cheapest Casas Particulares in Centro Habana...anywhere between CUC$20 and CUC$40 per room. I would recommend staying near San Lazaro/Galiano but anywhere in this area is great because it's the historic part of the city so you can walk everywhere.
Cuba doesn't have hostels per say..it's either hotels or casas particulares, which are private homes or spare rooms rented by local cubans. Hotels in Cuba are pricey so you can expect to pay around $100 a day. With casas, you can pay as little as $25 so you see the difference.