Since Brownsburg is close, just take it up to any house in Carmel & wash it there.
I don't think you will fit in a car wash, that arm in the middle of the ceiling for the water hose is going to hit. I wash mine in front of the house (on a cul de sac) on a week day after everyone has gone to work & it isn't trash day. I haven't seen any blue haired women but will keep my eye pealed for them. They might be peaking out the windows though.
We were in IN over the 4th & had a great time at Shipshewana, Turkey Run & McCormick's Creek. There is a great local buffet in Spencer if you ever camp down there, only $6 on Monday evenings.