Honestly, for a party that isn't all about the food, I go for easy. (Sometimes I want to have a fancy dinner party that is all about the food, but I don't think a 2 year old birthday party is the time)
Everyone likes dips. What about a simple veggie and dip tray? Fruit and dip? Hummus and baby carrots? Black bean dip or quacamole or salsa and chips? You can go all fancy and do the 7 layer Mexican dip with chips if you want. Or do the cheese ball thing. People love cheese balls. There is a chocolate chip one that is good with ginger snaps if you want something sweet or you can do a more savory one with crackers.
You can just put out a very, very simple not-Italian at all antipasto tray (we actually call it redneck antipasto
). Cheddar cheese cut up, summer sausage cut up, canned black olives, drained (everyone seems to love these in my family/friends), green olives if you like them, mini dill pickles if you want, then crackers. We like Kashi's TLC crackers or Trader Joe's multigrain, but do what you like. Sometimes I add marinated mushrooms. You put jarred mushrooms (the itty bitty button ones) in a jar of Italian dressing overnight, then drain and serve. They are suprisingly good.
I think I would go the route of having an appetizer set out when people get there or shortly after, then pizza, then dessert instead of finding something to go with pizza. The benefit of this is reducing (if not eliminating) the need for forks. Less stuff for you to wash later.
Hope you get lots of great ideas!