Hi,
If you have a Costco Membership or know someone with a Costco Membership, check out Costco's (Kirkland brand) Cooler Bag. It's pretty big though so not sure if it'll be too big for your needs. Sells at a good price. Cheap enough to throw away or give away if you don't want to take it home with you. If you see it, you should pick it up. The closer it gets to summer, these cooler bags sell out (at least in our neck of the woods).
As for the insulation of these bags, it is NOT premium insulation. However, it was sufficient for our needs (July in
Disneyland).
Hints:
* Freeze what you can before placing items into the cooler bags (eg. water bottles = pour some out and freeze)
* Examples of things we froze: water bottle, juice boxes, cheese sticks, yogurt tubes
* Chill well the unfrozen items (eg. we'd have frozen & non-frozen, well chilled water bottles)
* If you don't want to carry ice packs in the cooler bags, your frozen water bottles & juice boxes can help cool the cooler bag cool
* Also, if you don't want to carry ice packs, use good quality freezer bags (eg. Ziplock Brand Large Freezer Bags) and fill with ice. Double bag (ie. use 2 Freezer bags) the ice to help prevent leakage. You can always replace the melted ice with fresh ice in the park.
I originally used a smaller cooler bag (flat design) and found that it was too small. This was a Coleman brand cooler bag. Good insulation but too small for our needs. It was hard to dig for items and didn't fit much. It was easier to use the larger Costco Cooler Bag. The back of our stroller had a little step which we rested a corner of the bag on. This helped take some of the weight off the cooler handle (with the larger bag I put more stuff in the cooler).
Another Hint:
* Keep your child in the stroller or have someone hold onto the stroller UNTIL you remove the cooler bag off the handle. One time our child was so eager to get out of the stroller that he hopped out before we had a chance to remove the cooler and the entire stroller tipped over.
Good luck and have fun!