Hi Charlotte
I don't know anything about the diving side, but here are a few ideas for the cultural side:
The Hypogeum in Paola is an interesting place to visit, its a UNESCO World Heritage site and you can find out more information about it here:
Hypogeum infoIt is true what wiki says about it getting booked up quickly - particularly in peak season, so if you want to book online, you can do that here:
HypogeumMdina is also worth a visit
MdinaWe took a daytrip over to Gozo, it's a beautiful island. The ferry is situated in Cirkewwa on Malta and its really easy, only takes about half an hour to cross over and you can just turn up and buy a ticket for the next ferry. We went in February though, so there may be a slightly longer wait in full season I guess.
Hope you have a great time.