I was also going to suggest a corn salad or cucumber/tomato salad. Two of my summer favorites.

I also just started making a yummy pasta salad that would work as well (no mayo).

1/2 lb cooked pasta (I like to use something small)
1 pint cherry tomatoes, halved
3 mini cucumbers, chopped
couple good handfuls of baby arugula
1/2 cup toasted pine nuts (would probably leave these out for fear of allergies)
I also add chopped basil & parsley from my garden
salt & pepper
store bought balsamic salad dressing - Marzetti makes a really good one - to taste

It's really yummy!

I thought mayo was good left out?

Mayo really doesn't go bad if left out.
http://homecooking.about.com/od/howtocookwithcondiments/a/mayospoilage.htm

Pesto pasta salad

Fruit salad. Easy and kid friendly.

My go-to this summer has been tomato & cucumber salad. Dice tomatoes, dice cucumbers- toss with some olive oil, a splash of lemon juice, salt & pepper. Sometimes I'll also add some red onion, some black olives, or some summer squash.

Homemde mac n cheese.

Always the first thing to disappear at these types of things.

Watermelon is good too, but are they still in peak season for sweetness?

Say what you will about fancy food, when it comes down to it people prefer comfort food.

Watermelon slices are great.

My picnic go-to is corn salad - corn sliced off the cob, tossed with halved cherry tomatoes, diced red onion, and a bunch of fresh basil. Add EVOO and red wine vinegar, salt and pepper. Done. To spruce it up, you can also add arugula.

Our daycare center (infant through preschool) is having their summer picnic. The provide hot dogs and parents are bringing the sides. Something that can sit out is a plus (no mayo!!). My first thought it to keep it easy and bring watermelon slices. Any other recommendations? I don't mind preparing something the night before and swinging by the house to pick it up before heading over.