you'll probably have to stay in one of the suburbs and drive to--and-fro.

Check any of the major chains.   Indy is surrounded by areas with lots of lodging.    I'll probably stay in Noblesville

nowhere is cheap in the INDY region.  there are a few budget motels down in Franklin and some up nw in Lebanon. but they're nearly an hour from downtown.  probably OK if you are coming in for a one day visit. but too far if you are going to be there for a couple days.

Call around the major chains ask for Sr cit/Vet/AARP etc etc. discounts and haggle if you can. but it is a sellers market during bit special events.
There are motel coupon booklets for various regions of the country that can really save bucks but I find them mostly at highway tourist information center/rest stops.  But most motels have a limited number of first-come-first serve "coupon rate" rooms. (and they cannot be used with reservations--strictly walk-in).  I use them a lot whenever possible   (I stay in motels all over IN 12-15 nights /month year round)
if you stay in motels a lot you may be able to use "reward-points" for a free night stay; but some motels have "black-outs" for special events.   INdy500 weekend, the NASCAR weekend,  major sports tournaments etc---fugiddaboutit.  Stupor Bowl last year, I doubt you could find a room within 50 miles of downtown.