Greetings! You've probably found a way to wash your car already by this point but if not let me know what area of the city you moved to and I'll give a few tips. One of the most popular north of the river is the Olympic on N. Oak: 6220 N Oak Trafficway. They also have a location off of Shawnee Mission Pkwy in Kansas if that's more convenient.
Welcome to KC, and I'm sorry you had to move here