I have found the older ships have a far higher perdon to doace ratio. The newer ships have far more cabins but not proportionately more space. I would suggest having a look at a ship with capacity below 4000.
Hi we once did every port stop on a 7 day Caribbean cruise with out booking any excursions. You can walk around the local area, you can often get a hop on hop off bus tour, or hire a taxi into nearest town. Trust me you do not need to fork out for paid excursions. Yes come and go on the ship as often as you like. Research the local area yourself before you sail.