You may consider a carriage ride around Old San Juan if you dad can't walk far. You can then go to ElMoro fort - he may like that too.
In Nassau, you may take a water shuttle to Atlantis and if you pay $25, you may walk around their grounds and visit the DIG - the acquarium. The grounds are in fact impressive, even if you cannot use their pools.
In St. Thomas, we've booked a tour with Godfreytours, for $20 pp, he'll pick you up from the ship (at 9,10,11) and will drop you off in town to shop. Then at noon he'll pick you up from town (or ship if you skip shopping) and will take you on the tour of the island for 2 hrs after which you may go to a beach of your choice (Cokie, Meagans or Saphire) for 2 hrs and he will be back to get you. Or you can go back to the ship (I think...)
We don't know much about LaRomana/CasaDeCampo, but we're planning to visit an old Spanish town built years agon with CasaDeCampo. It's supposed to be amazing. I'll have more to report when we get back from our 1/19/03 MIllie cruise... I can't wait!