A good place right by the rail station and Minnehaha falls and park. Just get the Metro Transit app and, although it is a little more time consuming, save tons on not having a rental or paying for parking just about everywhere. You can even take the Metro blue line train to the 50th street Minnehaha Park Station from the airport and walk the 200 feet to the house. Super convenient.
Go to Matt's Burgers to get the Juicy Lucy, worth the time and wait in line.
And always be kind to the cat. She's a sweetheart. And if she tries to bite you it's really only a touch, she won't hurt you. And she does go outside when she wants to.