If you're traveling any distance, you want foods that will keep well without too much refrigeration. Then there's the question of utensils or not. I think picnics should be simple, not overdone. When we think of finger foods, we think of sandwiches. Suggest something wonderful.
Stuffed breads are a good sandwich alternative.
Depending on the number of people, you could hollow out one large round loaf, which would serve four to six, or individual rolls. The bottom layer should be something solid and absorbent, like lettuce, so the bread doesn't get soggy. It could also be good with portobello mushrooms, marinated with olive oil, garlic and a little lemon, grilled. Another idea would be your own rendition of a pain bagna. The classic is an anchovy or sardine sandwich on crusty French bread.