The iPad is great for games, if you search you should find some threads on this forum where people list their favourite games, there are so many. With the Air because of the extra physical space you have, I've found board games are even more fun (if you're a board game fan). Lots of others, though, there's a sister site to this, Touch Arcade (link at bottom of page), that reviews iOS games and has forums where people discuss the games, quite a good source of information.
Other iOS Apps (again, there's a link where people rank their top 2 apps and list them, search the forum here) to consider:
Dropbox (great, especially if you've got the 16GB)
Evernote (you'd be amazed the things you can use it for)
The Room 2 was just released, I'd get The Room (v1) first, then the second one, both are stunningly awesome games that are perfect for your iPad.
Enjoy your new purchase, and congrats!