7 days is better.

We have been to several cruises already (East, West Caribbean, Alaska, etc.). They are all very good. Nice view, nice food, nice service, nice shows. Very relax. We plan to take cruise again later (when my baby gets bigger). Grand cayman is a must-go place. 7 days cruise is better than 3-4 days since usually 7 days cruises are using bigger and newer cruise ships.

You don't need visa as long as you are US citizen or green card holder.