When Chloe and I are out and about, I am never without her foldable Ginsey Disney Princess Traveling Folding Potty ($12.69 at Diapers.com). I keep it in a large ziplock and it fits perfectly in my handbag or tote, as well as in her stroller. (It's small enough to fit in a Louis Vuitton Speedy 30.) This potty is great not only because it's compact, it makes it easier for Chloe sit and use public toilet seats. I used to hold her over one side of a large toilet seat and pray my arms didn't give in while she peed. Now she can sit perfectly on her own seat! (I always place a paper seat cover and then place her foldable seat on top.) It's easy for her to use. We had other covers that were not comfortable and were so big to carry around. This one is the best!
There are lots of designs out there depending on what your kiddo is into. Diapers.com sells ones with designs from Disney Fairies, Winnie the Pooh, and Cars.