First of all, congrats on the wedding, and money not being much of an issue!!! How fun!!!
Hubby and I went to Puerto Vaillarta for 10 days at an all-inclusive, but we went the all-inclusive route BECAUSE of money...I preferred to pay up front and not have to worry about penny-pinching while we were there.
As far as "lots of activities, but not too cheesy" that is a little harder to come by. Most of the resorts, especially the ones I've heard of in Jamaica who advertise lots of fun activities seem to be ultra cheesy. HOwever, we were really happy with our package broker (Town and Country Tours). They met us at the airport, made sure we got into the "right" taxi to the hotel, and another representative met us at the hotel to make sure check-in went well and to provide us with a list of activities (NOT RELATED TO THE HOTEL) that we could do. This was PERFECT for us. Every other day we went on one of the trips...one was a cruise to a coastal village, complete with diving off the boat to swim with the fish, and my favorite, a full-day horesback riding trip into the jungle. Most of the "cheese" we encountered had to do with the guides on these trips trying desperately to get us to drink...think stupid college drinking games (perhaps they thought it would help their tips?) and the nightly "shows" at the hotel, although, our particular resort catered to middle-aged Europeans, so it fit more with their demographics.
(We chose the hotel, THIS IS NOT A JOKE!!, because the honeymoon fell in the middle of the Stanley Cup Playoffs, and it was the only one that guaranteed us it carried ESPN)
Definitely find a travel agent you like who can give you the inside scoop. It you go the Mexico route, try Cancun. It was too expensive for us, but my parents went the same year we did, and it seems to have more class and adventurous day activities like snorkeling and trips to see Mayan ruins.(They ended up using Town and Country Tours and had a similar positive experience)