A good place to get some info:
http://www.indy.org.
Events that are going on in the city during your stay:
http://www.indy.org/indianapolis/we....jsp?c=eventscalendar:all&p=1&x=1192720821240
A place to eat and not miss:
Bazbeaux Pizza. Great pizza place! It's an unusual pizza place. Not too many pizza places offer Albacore Tuna, Avocado, Snow Pea Pods, Fresh Goat Cheese, Black Bean Dip and other exotic items for toppings.
They also have the usual toppings.
They also have sanwiches and desserts like TARTUFO – Classic tartufo with a zabaglione cream center, covered by chocolate gelato,
crushed caramelized hazelnuts and cocoa powder and SORBETTI.
Another Indy restaurant:
The Milano Inn. Nice Italian place.
For Kosher food: try
Shapiro's Delicatessen. Voted one of the 10 best places to eat authentic Jewish deli cuisine but USA Today.
For a great steak dinner:
St. Elmo Steak House.
Of course, there's the usual chain restaurants downtown like Hard Rock Cafe, McDonalds, Alcatraz Brewing Co, Buca di Beppo, Buffalo Wild Wings, Le Peep, McCormick & Schmick's Seafood, Qdoba Mexican Grill, Rock Bottom, T.G.I. Friday's, etc.
For shopping, there is the
Circle Centre Mall right Downtown. It also has a theater and a game area on the 4th floor.
There is also
Broad Ripple Village. It's not too far from the downtown area.
For some History:
The President Benjamin Harrison Home. Only about 1 mile north of the circle.
There is
Historic Landmarks Foundation of Indiana which offers walking tours in Indianapolis.
Museums:
Eiteljorg Museum of American Indians & Western Art
Indiana State Museum
Which includes and IMAX theater.
Indianapolis Motor Speedway Hall of Fame Museum
Indianapolis Museum of Art
There are tons of things to do right in the downtown area. Another site that offer info on just the downtown area is
http://www.indydt.com.
White River State Park is right downtown. It includes the Eiteljorg Museum, the Indianapolis Zoo and outdoor concert venue the Lawn. There are gardens, Military Park, the Canal where you can walk, ride rental bikes, take a gondola ride or rent a pedal boat.
There's lots more info in the links I've provided.
There is also the
Iron Skillet. It features a traditional Hoosier menu.
For a local only Greek place,
Greek Islands Restaurant. They also have belly dancing on Friday and Saturday nights.
Heidelberg Haus is also locally and family owned. Great place for desserts. It's actually a cafe and gift shop with limited seating and they encourage sitting with strangers and making friends.
For more Sweets and desserts, there is the
Chocolate Cafe which is owned and operated by
The South Bend Chocolate Company. This is based out of Northern Indiana but now has a couple locations in Michigan and Ohio as well as Indiana.
For nightlife:
Comedy clubs
One-Liners and
Crackers are great places.
This link
http://www.indy.org/indianapolis/we...sp?c=nightlife:loungebars&p=1&x=1192727147725 privides a lot of info on the bars in the area.
I have provides links to all restaurants I have listed.
I had visions of organic food served in a comfy atmosphere. In the photos there are a lot of young women dancing around and posing in bikinis. 
when I am there!
