A cruise is a wonderful idea, and Royal Caribbean or Carnival would be a good cruise line for you and your wife.
Will you be doing other things in the U.S. in addition to going on the cruise? Coming all the way from India for such a short 3 or 4 day cruise seems like a long way to travel for a short cruise.
I'm not sure what papers you would need to travel here or to visit the countries your cruise will be visiting. You may want to check with your embassy or consulate to get that information, once you know which cruise you will be taking and which countries it visits.