There are many hotels in downtown Indianapolis at every variety of price points.
The closest major hotel to the wedding venue is the newly opened Bottleworks Hotel, located in a beautiful art deco building formerly home to the Coca-Cola bottling plant. It runs about $300 a night. This location puts you right at the north end of the Mass Ave cultural district, near a number of new (and old favorite) restaurants.
You could also consider the Hilton Garden Inn downtown, located just off Monument Circle, the historic center of the city. It runs about $130 a night. Another interesting downtown hotel is the Crowne Plaza, which occupies the parts of Indianapolis Union Station not currently used by Amtrak. This hotel boasts a few rooms in old former sleeper rail cars — the rooms themselves are what you’d expect in any hotel, they do not retain their historic interiors — but the novelty was nonetheless something Ben really enjoyed as a kid. The Crowne Plaza runs $150–$200 a night.
Of course, as a medium-large city that does significant convention business, there are the full set of each hotel chain’s brands in and around downtown. There are no shortage of places to stay in Indianapolis, both downtown and throughout the city. Plenty of hotels further out will be even lighter on the pocketbook, but we would recommend against booking anything on the far north/northeast sides (or suburbs such as Fishers) as that area often has the most traffic and the fewest alternate routes downtown.
A note about Airbnb/VRBO: We and our friends have encountered a variety of experiences with these apps, not all of them great. Because of this, we do suggest if you take that route that you stay near (or between) Meridian Street and College Avenue near downtown or farther north up to Broad Ripple.