I took Gracie Ruth and Yogi both out shopping with me before their shots were done. I just made sure to carry them, and not to let other people touch them and to keep the outing short enough that a potty break would not be needed. This got them out of the house, got them seeing new sights and kept us from getting cabin fever.
And I love our car seats. They can be up high enough to see out the window and yet are fastened securely in their seat. Just be sure to use a harness, not a collar to fasten them with. Here's a picture of Gracie saying, "Hurry up Momma and lets go shopping!"