I'd just let them run around in the backyard with some balls, use a bubble machine for bubble fun, maybe have playdough on a table and paper and crayons for drawing/colouring fun. All of that is pretty cheap.
As for food just do fairy bread, frankfurts (maybe in little rolls, but not necessarily), mini pizzas (cook from frozen) and fruit & jelly in plastic cups for dessert with the cake.
Definitely morning too. Some 3yo's have afternoon naps and it's not worth trying to have a party during nap time - could end in disaster.
And keep it simple. 3yo's won't even remember the party for long, they are still pretty little. And I'm another one that hates playcentres.