Hi C.,
My son turned 4 in June, and we hosted his party at Chuck E. Cheese. We had about 12 kids, and it cost under $200. We had the party on a Saturday from 4 - 6 pm because of the nap issue (we also have two other kids, age 1 and 2). That time worked out well for a lot of families. The kids had pizza and cake, which I'm sure sufficed for their dinners. We also bought the $1.99 Chuck E. Cheese goody bags, which were nice. I also bought 2 large pizzas and sodas for the adults accompanying their kids.
In the long run, I actually think it was cheaper than having a party at home, because you still have to buy food, drinks, party decoratons, etc. You also have to worry about games, goody bags, etc. When our other child turned 2 in May, we had a barbeque, and by the time we bought all of the food and drinks, it added up to at least what we spent at Chuck E. Cheese's (and we didn't have any formal games, but there were toys everywhere). The clean up was monumental--lots more work.
It is not at all horrible to have a party at home; we've been to those, too, and they are nice. It is just a lot of work on the family hosting it.
Good luck, and try to enjoy it!
R.