I usually don't think of the Indianapolis area when it comes to Cajun food, but IMHO Mudbugs Cajun Cafe in downtown Carmel is really excellent. The atmosphere is a little strip mall, but the price point is decent, the service is fantastic, and the food is fairly authentic and consistently delicous.
The dirty rice, shrimp etouffe, pork po boy and crawfish casserole are among my favorites. If it's your first time, make sure you tell them. They'll give you a free sampler platter--a little bit of a taste of about seven items from their menu.
If you have kids who won't eat cajun food, they offer a chicken finger meal (but I think you have to ask for it--it's not on the menu).
Carmel's downtown has developed into a really cute area with shops and a really nice vibe, so you can walk around after/before you eat. Mudbugs also has outdoor seating--although again, not the greatest atmosphere, but some pretty good people watching.
They also serve bottled beers. Carmel's about thirty minutes from downtown Indy--I never thought I'd say it, but if you want Cajun in Indianapolis, Mudbugs is worth your drive.