Let me start out by saying that when me & my fiance first starting dating I took him on his first cruise (as his Christmas gift) on a 4-night Carnival cruise to the Bahamas (we had stops in Nassau & Freeport). It was enough to get him hooked! We've taken a handful of cruise since then & he's LOVED them all! We're getting married next april on a cruise (it will be my 7th & his 5th cruise).
We've already been talking about what our 1-year anniversary cruise will be...and there just so happens to be a Hawaii cruise (15 nights!) out of San Diego...that will fall just before the 1 year anniversary marker!
All of our cruises have been Carnival, with the exception of one was NCL. The whole trip we kept comparing everything to Carnival (maybe because it's what was familiar to us?). But we vowed only to do Carnival going forward! The shorter Bahamas cruise is a great introduction to cruising though! And you should be able to get them pretty cheap too!
If you convice him to take a cruise...my advice is to sign up for excursions in ALL ports! They're well worth the money to have activities planned! And you get to see much more of the island than you would if you ventured out on your own! Let me know if you have any questions!