Hi Pomerenke,
I'm surprised there aren't 4 pages of responses to your question already.
From my perspective, there is so much personal preference involved that your is a very hard question to answer. With that being said, I'll give you my perspective.
Of the three, I'd cross Cozumel off your list. That's not to say Cozumel isn't great, because it is. I'm in fact headed there later this month. But because you want to do both land activities and diving I'd leave Cozumel off. The diving there is very fun and very easy but I don't get too excited by the land activities. In my opinion there isn't enough on the island to spend a week exploring. Granted, Playa is a short ferry ride right across the channel and Cancun is close too. But, both of those places are overly touristy to me. There is very little there that I find "authentic". However for a future trip, if you've never been, you should add Cozumel to your to-do list.
As for the other two, I would tell you to go to Thailand. But only because I've never been and, Thailand has been on my diving bucket list for a long time. Again, there is that personal preference sneaking in. I'm sure you've done a lot of research on the diving there. It's supposed to be world class and from most of the people I have spoken with they agree with that assessment. Thailand I also believe would suit itself well to a liveaboard.
I've been to Belize a few times and, so far, it's my favorite stop as far as the combination of land and sea activities go. You could easily book a trip on one of the liveaboards there. That will probably give you the most diverse diving experience. But, you could also choose to stay on Ambergris Caye or Caye Caulker for your "diving" week. Dive sites are a very short boat ride from the beach.
A few years back, my new bride and I honeymooned in Belize and did something similar to what you've described. We spent a week inland at
Cave's Branch visiting Mayan ruins, repelling off of cliffs, exploring the ATM cave, etc.. It was fantastic. Then we flew to Ambergris Caye and partied on the island between diving.
Best of luck to you, it's not an easy decision you're faced with. Like I said, I'd jump at the chance to do a Thailand trip. But, I also don't think you can go wrong with Belize.