If you don't feel like springing for St. Elmo's, Harry & Izzy's next door has the shrimp cocktail, too. The place is owned by the St. Elmo's folks and, of course, Peyton Manning.
The whole Mass. Ave. stretch is cool if you're arty, or even if you're not. A lot of little funky places. As for Broad Ripple, Plump's Last Shot is full of Indiana high school memorbilia, what with the place being owned by the legendary Bobby Plump, who hangs there often. (Aside on Bobby Plump: a friend of mine told me the story of how he recently was on the Hinkle floor with Plump for a Butler event, with Plump pointing out the exact spot on the floor where he hit his famed shot. Then Plump hit nine of 10 in street clothes from about 15 feet out. Not bad for a 70-year-old.)
Other good eating spots: the Rathskeller (in the Athaneum, on the Mass Ave stretch), and, in a shameless plug, Jockamo's Upper Crust in Irvington (east side), which should be open by then. It's owned by a good friend of mine who managed the Broad Ripple location of Bazbeaux's for a long time. (He's have an opening party in mid-October, so I presume the restaurant itself might be open by the end of the month.) He's really been responsible for a lot of Bazbeaux's success the last decade, and I'm not just saying that because he always grabs the really good beer from the restaurant when we're getting together to drink.
Speaking of high school hoops, some teams might be starting up that weekend. It might be fun to take in a game, preferably in one of the rural schools outside Indianapolis. It might not be quite like it used to be, but Indiana high school ball is still special.
Also, the art museum there is good, and just had a big expansion, I believe. That's northwest. Another popular tourist spot is Conner Prairie in Fishers, which is an 1836 village with actors recreating life at that time. It's a lot less cheesy than it sounds. Plus, it has a thing where you and other tourists play escaped slaves looking for spots along the Underground Railroad.
