My first suggestion: Check the events section at VisitIndy.com to see what is happening. This weekend is the Circle City Classic and a Colts game. This is great information to help them avoid the traffic and maximize their time experiencing our city and not sitting in traffic.
Start at Keystone at the Crossing with brunch at Cafe Patachou before shopping at the Fashion Mall. And right now, make sure you use the entrance at River Road next to Maggiano's and not the main entrance to avoid all that construction traffic!
Shop until you drop, then enjoy the drive downtown. When you exit the Fashion Mall on 86th Street, turn right and go 2.4 miles to Meridian Street. Turn left on Meridian and experience "One of America's Most Beautiful Streets." Along the way you will see Second Presbyterian Church, which received the world's attention during Ryan White's funeral and the Governor's Mansion at the NW corner of 46th and Meridian. Don't miss my favorite home at 4356 N. Meridian Street. (below)
After checking in and relaxing for a bit I would head out to enjoy Indy! Here is where I am torn on two different suggestions.
Option 1: Dinner at St Elmo's followed by drinks and live music at the Slippery Noodle. The challenge with this is that St Elmo's has a Sunday menu that is all but impossible for a vegetarian.
Option 2: Take a cab to 45 Degrees on Mass Ave for a pre-dinner drink. Then walk half a block to Mesh for dinner. (awesome patio with fireplace) Then perhaps an after dinner drink at Tini. The challenge with this option is there is no live music in the Biergarten at the Rathskeller on Sunday night.
After sleeping in on Monday morning, I would take a walk over to the canal and have lunch outside at Creation Cafe.
What would you suggest for 24 hours in Indy?