We have an insulated picnic basket that we love to take to the park or to play dates. I throw an ice pack or two in with our food, and it lasts just fine. Some of our grain-free picnic food includes:
Cheese cubes
Applegate Farms lunch meat
Grapes, apples, or other fruits that I can put into a jar or tub for travel
Grain-free crackers with cheese or nut butter
Almonds, pistachios, or other nuts
Applesauce
A thermos of soup (we do this a lot actually when going to dh’s worship rehearsals)
Baby carrots, celery
Hummus
We even do Boulder kettle chips on occasion. They’re made from potatoes! I don’t like the oil they use, but these are a rare treat for us.
Our family does not care for cold salads, but potato salad, cole slaw, chicken salad, carrot-raisin salad, and such would be good too. We just don’t like them.
Hope that gives you some ideas!