I recall that the fast food industry was just in its infant stage. McDonald's was a "new" craze, and Burger King was just getting started too. Families just didn't frequent restaurants and fast food joints as often as they do today. When I think of a typical 60's or 70's meal, one word comes to mind. STARCH! A true meat and potatoes period in time, with Holidays being the time to roll out the special Jell-O mold. It was inevitably green, and filled with things your mother otherwise never served.
Have a good supply of candies on hand, like string licorice for peace signs, and Necco wafers or PEZ candies for flower designs.
That said, I feel the field is wide open at your Groovy Girl party to serve foods that you WISH were served in the good old days. Serve pizza, loaded hoagie sandwiches, a Mexican taco bar, flower-shaped sandwiches made with a cookie cutter, your options are unlimited. The only thing that wouldn't be appropriate for a Groovy Girls theme would be a formal meal.
If the party is for a child, and you are serving dinner, let the birthday boy or girl choose his/her favorites. I generally recommend that unless you are having a sleepover party, that you avoid scheduling a party around times that would need to include a meal. Serving snacks, birthday cake and ice cream, along with beverages is plenty.
Regardless of the ages of your guests, however, I do recommend that you include a theme cake to your dessert menu. Try either a Flower Power Cake, Butterfly Cake or Smiley Face Cake, one of these will bring big smiles.