Sandwiches are one of the easiest party foods to prepare without spending a lot of cheese. Toddlers will especially like the offering since it's something familiar and easy to nibble on. Peanut butter and jelly is a classic way to go (minding any peanut allergies), although feel free to spice them up with different jams, banana slices and cut strawberries. Likewise, deli turkey and ham with optional cheddar or Swiss slices are sure to satisfy.
If you're concerned that sandwiches on a plate look too humdrum for the festive occasion, get out the cookie cutters. Although you'll waste a bit of bread, the fun shapes can coordinate to the party theme and entertain the hungry guests.