The caribbean be cheaper for you than Hawaii, with you being in Chicago area. There be regional airlines flying down to Orlando area for a competitive price. From there ye can drive down to the keys or take a low cost cruise.
The caribbean being more expensive "flight wise" for us on the West coast. About a grand a person if ye don't plan ahead. Hawaii on the other hand costs less for us (as low as $200 sometimes) and we have direct flights (yep, straight from Phoenix to the Islands.)
As far as accommodations go, that I don't know. I spent a week at a condo (2 bd, 2 bath - extra kid slept on couch) and spent the same amount for a beach house in santa cruz, ca (3bd, 2 bath). So I guess it is more expensive. I cruised the caribbean, so I didn't have to worry about accommodations, cooking or cleaning. This is probably why I prefer the caribbean. There is only one cruise line for the Hawaiian Islands and it isn't very good (no a/c).