Hi S.!
I haven't had a party there, but as someone that has attended a few at Chuck E. Cheese, I would say no. It is really loud and no one can hear themselves think. Most of the games are not geared for preschoolers (unless they have made changes since the last time I was there). I would still check it out, but I have another idea for you if you live in the Medina area.
I just had my 5 year old daughter's preschool b-day party at Rockin R.'s Amazone in Medina. It is a large jungle gym type thing (think McDonalds' play land times 10!), and the general set-up is better than Chuck E. Cheese's. It also has an arcade and laser tag, but they are in a separate area from the jungle gym. They have party tables there and food, etc. and they let you bring in your own cake.
We held the party on a Friday after preschool; school let out at noon, everyone was on there own for lunch and we had the party from 1:30-3:30. It was a great way to keep the costs down (i.e. I didn't have to pay for all of the kids and their parents to eat!) and let the kids unwind from school before charging them back up again! We paid for all of the kids from hr preschool class and siblings were welcome at the parents’ expense.
You can check them out online if they are in your area at http://www.myamazone.com/. Whether it is right fit for you, I don’t know, but I totally get the not wanting to hold it at your house thing. The kids loved Amazone (they are still talking about it!) and it was quick and easy. Good luck in your decision!