I don't have a picture but mine is a soft sided one that can hold 6 cans of soda. Basically a square lunch cooler? It fits easily in the bottom of our stroller and we've never been questioned about bringing it in.
We also have a back pack type diaper bag by Baby Trend that has an insulated compartment so we 'smuggle' water bottles in it! And even though we won't need that bag for diapers this year, we'll be bringing it along!