Might have been a good idea to put this in the Travel/Housing/Dining subforum for visibility. I know drinking isn't exactly "dining", but it sort of fits the spirit.
Anyway, can't speak to karaoke in Indy. But as far as bars are concerned:
- Nicky Blaine's. It's actually a "cigar bar", but it's definitely also a nightclub with drinks and even a bit of food. It'll probably feel untouched and unaffected by the convention, but it's just a really cool spot. I like going there when I'm in Indy (I get there every few months or so for business). It'll function as a semi-classy escape venue, if you want to get out of the con atmosphere for a bit.
- The RAM. This'll be the opposite of Nicky Blaine's in that they'll go all-in on the Gen Con theme. I'm stretching the definition of "bar" here, BTW - they're really a brewpub, therefore as much restaurant as they are a bar - but it's worth a stop for non-national brewery beer and some food while staying immersed in the Gen Con atmosphere.
- Slippery Noodle Inn. They're popular among Indianapolis NFL fans, probably because they're less than 3 blocks away from the stadium. They'll have live bands going each night. I have no idea if they'll be in on the Gen Con themeing or not, but I'd actually guess not, since they have their own vibe going.
- Claddagh. Irish pub. Yeah, it's a chain, but it doesn't feel chain-y, not to me at least. On Saturday they'll have live music. I'm a bit biased towards liking Irish pubs, but from speaking with locals, I'm not alone in liking this place.
- The Rathskeller. Again, naming a restaurant. Why? Well, for one they have a biergarten. For two, they feel more like a venue that has an area for drinking (the "Kellerbar"), an area for live music (the afore mentioned biergarten, which is still also a bar area), and an area for a full sit down dinner, so you can do the drinking aspect if you feel like it. Or you could get stuffed silly on schnitzel before downing lagers, weiss's, or whatever suits you. It's genuinely worth going to.
- Plat 99. This one's my out-of-left-field recommendation. On the one hand, it's just the bar/lounge for the Alexander hotel. On the other, it's a genuinely nice, relaxed cocktail bar that isn't crowded at all, isn't going to feel like it's even aware of Gen Con, but is a decent place for some good mixed drinks in a chill atmosphere. You won't get much of a beer selection there, but if you're into cocktails, it's definitely a good stop.
I can come up with more, but that's a start. And with the exception of the Slippery Noodle Inn (of which I've only been told about), I've been to every one of these places more than once, and outside of Gen Con.
Hope that helps.