Probably one of the best campgrounds in the Indianapolis area is actually not in Indianapolis. Oh, you can stay at the Indiana State Fair campground and be in the middle of suburbia, but if you want something that's more natural White River Campground near Cicero, Indiana is probably the best campground around, next to the State Parks. It's located about 30 miles north of Indianapolis, but it will put you close enough to just about everything, you'll have no problem making day trips.
Click here.As far as attractions, Hamilton County, Indiana has just about anything you can imagine. I've lived in this area all my life and the activities just keep increasing. Everything from Conner Prairie Settlement on Allisonville Road South of Noblesville, to the Monon Center in Carmel with their indoor water park. Activities, shops, restraunts, events, you name it. Carmel, Noblesville, Zionsville, Fishers all have historical districts, city and county parks, and lots and lots of places you can part with your money. Then retreat at the end of the day back to White River Campground and get away from all the hustle and bustle.
Exploring Hamilton County alone, and you won't even have time to touch Indianapolis. Indianapolis has the Childrens Museum, Speedway (where they run the Indianapolis 500), and the down-town Circle Center Mall just to name a few.
Click here and this will just touch the surface.