My first-born and I spent a lot of time at The Museum of Fine Arts in Boston. In addition to the endless colors and shapes, the miles of smooth floors were perfect for my fledgling walker. Of course, going anywhere in public with a toddler always presented the possibility of a dirty diaper...
My diaper kit was a variation on my brother's idea. He used to simply stuff a diaper in his back pocket before taking his child out on the town. When I asked what he planned to do if there was more than pee to deal with, he said that he would simply ask any parent around for a wipe.
This seemed a bit too casual and unpredictable to me, so I came up with a neat little trick. Before leaving with my son on an outing, I opened a single diaper, put a few wipes in it, folded it back up, compressed it and put it in a sandwhich bad. I carried this in my back pocket. I also made it a point to carry a pair of latex gloves on me, just in case.
In addition to being light, this "emergency preparedness kit" did not interfere with my mobility and I got the peace of mind of not having to carry around a lot of "stuff."