I like bringing my rat over to my mom's house for brunch. Mom lets me put her carrier on the table and Nanook comes out and samples the pancakes and fruit. It's pretty fun.
I've also taken her to an open air market where everyone fussed over how pretty she is.
Most frequently we go for evening walks around the neighborhood. I'm always slightly concerned that a hawk might grab her off my shoulder, so she hides under my hair or else I end up holding her in my arms (which she loves!).