At Casa Mildred y Gonzalito. You'll have your private room in an apartment with local Cubans. The first breakfast (for two) is included in the price!
The apartment has a balcony looking towards the street, very comfortable, clean and safe.
Location wise it is extremely centric: just a stone's throw away from the Malecon, 5 minutes away from La Casa de la Musica, 10 minutes away from Old Havana.