I don't know your area, but I do know that 95% of parties for kids under 5 are really doomed if there is too much structure and too much attention required. Kids that age don't understand birthdays (the birthday child doesn't get it, and the guests don't understand why they don't get presents and have to sit and watch someone else get everything). They don't like big groups, and barely have any experience even in preschool with a skilled teacher. Even in preschool, each "station" or activity lasts 15 minutes at most. Most kids do much much better at a small, free-play home party that lasts 90 minutes at most. Free play, small art activity (very simple and open to individual wishes - maybe sticking some feathers and goggly eyes on a piece of poster board, or foam shapes on a foam picture frame), then snack (or birthday cake/cupcakes with singing of "Happy Birthday"), then more play, then go home. You can have the birthday child open 2-3 gifts tops from 2-3 friends, and give the friends a party favor or goody bag. That's it - they're done. Anything more than that becomes so frustrating for the parent, the guests and the birthday child. They don't play games well, don't understand rules, don't like to wait in line for their turn, and so on. They certainly don't understand themes and decorations, and they don't care. If you can have them run around outside or in a large finished basement, that's a bonus.
If you really don't want it at your house, then find a restaurant that will let you give the kids whatever they want and run around - there's not much in that category except McDonald's and similar fast food places, which is a problem. Maybe you can rent out a small section of a church hall or other community place like the Y. You provide the food and clean-up, and pay a small fee for the space and the existing toys.
I'm not sure why this place you have picked out is not calling you back. Maybe they aren't in business? Maybe they just don't do parties with such a young crowd? Maybe you should save a cooking program for when your son is 6 or so?
All I know from everyone on Mamapedia is that younger kids do best in small settings with limited expectations from the grown-ups, in a short party where they don't have to stay for too long. You can have 1 or 2 friends stay with you unless you have all the parents stay, but even so, you have to make sure they don't all come with the other siblings, because that spells "chaos"!!