Coxhall Gardens, located off of 116th Street in Carmel, Hamilton County, is one of the most popular spots for elopements!  It's very popular with photographers for engagement and family photo's too!  It's free to use but you can also pay to reserve the Centerpiece.  The Ritz Charles also has an even area so you will want to make sure you aren't eloping at the same time a large, formal, wedding has the large amphitheater reserved.  Once, in the past few years, someone has rented the entire park, so you will want to make a call just to make sure everything goes smoothly on the day you choose. 

There is a large picnic shelter that you can rent if you wanted to have a larger, informal wedding too!

https://www.hamiltoncounty.in.gov/facilities/facility/details/coxhall-gardens-3

My fee to marry you at Coxhall Gardens is $150