Do not pass Go, do not collect $200 until you have been to the Irish Lion pub in Bloomington. Mister is from up there, and we get up there every so often. It's one of my favorite restaurants ever. Mister has also taken me to the Trojan Horse (Greek food, obviously), and a little place called the Runcible Spoon. There's another restaurant he's been to, but I haven't, called Little Zagreb. Yep, it's Eastern European food, and he says it's pretty good.
When you go to the Irish Lion, make sure to look in the window at the Smith-Holden Music Shop. It's always closed by the time I get there, so I've never been in, but there's some nice guitars on display. It's just a couple doors down from the restaurant - usually where we park!
When Mister was living there back in the bad ol' 70s, they had a pretty big coffeehouse scene going on in Bloomington - college town, of course. What the music scene is like there now, I can't say. Others have already mentioned Bean Blossom. Bloomington is also nice for shopping - they still have locally owned shops on the square.
I'm not real familiar with Indy proper, but I have been to the Eiteljorg Museum, and enjoyed it very much. Also, if you like auto racing, there's plenty of that to go around (no pun intended).
If you like history, visit Conner Prairie. It's an 1830's living history museum where they've taken old buildings and moved them to the site. They have a pretty nice restaurant too! They also do special events at the holidays.