Hi, Marsha. Used to live in Indy and still visit there frequently. In fact, spent a weekend last January with a couple of VR pals named Janie and Gina
Anyway, there are two extremely upscale hotels: The Canterbury and The Conrad that are right downtown. There are many other nice hotels, which you can check out at this link: http://www.mytravelguide.com/hotels/cthotels.jsp?objectid=7612001&referral_id=YHOOPI&referral_click_id=CITYHTL|7612001
For dining, definitely check out St. Elmo's Steak House, which is also downtown somewhere, Illinois St., I believe. Other good choices are 14 West, The Palomino, The Eagle's Nest, and The Oceanaire. Here's another link to other downtown restaurants:
http://www.indydt.com/restaurantresultstemplate.asp?RestaurantType=Full+Service&Type=Category
The State Museum is also downtown and a real treat to see, plus The Eiteljorg Museum of Southwest art. The Circle Center Mall is also downtown and within walking distance of all the major hotels. If you get a chance The Indianapolis Speedway Museum is about a 15-20 minute drive west of the downtown. Any hotel employee could direct you there.
There are plenty of other places up on the northside of the city and in the Broad Ripple area (really artsy). If you're not staying downtown, send me a pm, and I'll give you more info about other sides of town. Have fun. Indy is one of my favorite big cities.