We have taken several of our rats with us. We've even snuck Jazmyne in the store when she was little. She slept in my fiancee's hood the whole time. They've gone to the petstore with us (since SDA isn't around here) although it is only occasional. They've been to the movie rental place, two malls, the park, etc.
One thing you'll want to be careful for is the car ride itself. Make sure your rat is somewhere secure. If you ever have to hit the brakes quickly, your rattie might go flying. Which I am sure hurts!
Depending on what area you live in, you might want to avoid the petstore. SDA for instance is an airborne virus they can catch just from being in the store. It can also be transfered if they come into contact with the virus if you come home less than 3 hours after exposure to it yourself (it 'rides' on your clothes, shoes, etc), or to other rats who have SDA.
SDA, if not caught in time and treated with strong anti-biotics, is usually fatal.