Where do you want to go? Cuba is not that small.
I recommend Santiago de Cuba, since climate and people are hotter and everything is MUCH cheaper than in La Havana. Flights are also less expensive, 220$ to Santiago, 300$ to La Havana, both roundtrip from Santo Domingo. If you are interested, check for available direct flights to Santiago, last month the only destination from DR was La Havana. According to my travel agency that might have changed now (Emely Tours, Av. Tiradentes Esq. Roberto Pastoriza, Plaza JR, Santo Domingo, 566-4545).
In your tourist visa you always have to put a Hotel name or a non clandestine private house (casa particular). I always put in "Hotel Santiago" and was never asked to show the reservation. In reality I stayed in a casa particular. If you want I can give you address and telephone number of houses in Santiago and La Havana all in the $20-$25 range.
Final recom: stay 10 days instead of a week!
Enjoy your stay.