Yes you can travel around with your Cuban boyfriend in a rental car, cab or bus, if you are going to do extensive travel I recommend rent a car, but if you are just going to a couple major city you are better of taking the Via Azul bus is cheaper and you do not have to worry about the driving and between major city you could get share cab, that even better, if you decide to rent a car put your name and your boyfriend on the lease, that way you both could drive the car without penalty.
go luck and if you need any further help let me know, I also have a Bed and Breakfast in Trinidad if you need a place to stay when you there, see my ad in this website classified.
