I have been to Punta Cana 6 times. Obviously I love it there. The beach is beautiful, the food is fantastic and the people are very friendly. I have not had the problems of people hounding you as some have mentioned. You can rent scooters, buggies and four wheelers there. I have seen the odd sport bike when out in the little cities. I have only stayed at 5 star resorts, so you kind of get what you pay for I think.
I have not gone to Cuba because of the bad reviews on the food. (Food is a huge part of my vacations) My mother has travelled to Cuba twice a year for the last 15 years up to about 4 years ago and she said it has really gone down hill. 4 star resort she was at ran out of food half way through her holiday. They were letting a lot of locals in at the resort she stayed at just to fill the rooms. She said it was never like that before. Beaches do look beautiful there though.
If price is an issue I think Cuba is the cheapest. Puerta Plata is cheaper than Punta Cana.
Sister just came back from VH Gran Ventana in Puerta Plata, she said it was good for the money and you are close to a little shopping area and night club that was a lot of fun.
I'm jealous.....I want to go! (How big is your suitcase? Can I fit?)
Have a good time wherever it is you choose.