C.L.
My 3 year old is also in preschool. I had a rough time at first packing lunches for her. She goes to a Montosorri school, which means the kids get out their own lunches, open them, eat, and clean up mostly on their own. So I get a double challenge as some foods (like hard boiled eggs) are very hard to clean up.
My daughter also doesn't like sandwiches, so I'm in the same boat. Here are some things I send in her lunch:
Apple slices
Grapes
Cheese (either string or just cubed)
Lunch meat (rolled)
Peas and corn (she likes these cold)
Milk (in a metal bottle that I wash)
Soup (thermos)
Chicken nuggets (thermos)
Pasta salad
Plain pasta
Good luck. One of the blessings of having a toddler is they will chow down the same thing day after day. So try not to worry to much about variety.