My son is 2 1/2 and I did his 2nd B-day at Chuck E Cheese, and it went great! It was very easy, and nothing to clean up. It is his favorite place, we go there all the time. We mostly stay in the toddler area, and he goes on the slide and stuff (great place for winter with young kids... its like an indoor playground, and until they discover tokens, it is free!). My son has now discovered the games... and LOVES it! He may not win, but he doesn't know the difference. Skee ball is one of the best, I will just play it with him, and let him roll the balls. He thinks it is so neat. When I have older kids with (usually a 9 yr old if any), they will take him up in the tubes for the bigger kids (I don't let him go alone... kids can get mean up there), and he just LOVES that! Or else an adult can go up there with them too... but I don't anymore, even at 23 it is too hard on my knees. If your not sure how your son will do there, try taking him there sometime soon, and see how it goes. I bet he will love it!
Another good place for birthday parties is Pump it Up. I am thinking about doing that for my sons next party. It is an indoor play area with inflatable stuff to climb on, and slides, and a ton of stuff. You get some time in the party room, and then in the play area (and they also have people watch the kids so you don't have to worry too much). That is in Burnsville, off of Cliff Rd. Not sure you would want to come that far... but I thought it was amazing when I went there! I would definitely look into that.
When I was little, we did McDonald's parties, and got food and cake from there, and then the kids all got to play in the play area, and that was really fun too. The McDonald's on Nicollet in Burnsville has a great toddler play area! Don't know of any other's good for younger kids, but I am sure in Minneapolis you can find one.
We also a couple times would rent a hotel room, like a poolside room at a Super 8. Then everyone could go swimming, and there was an open area we could run around on the other side of the pool area. We would have snacks in the room for whenever we wanted them, and that is one of my best memories from when I was younger. And then you can stay there that night (even let him stay up a little late swimming!), and any close friends could spend the night too, maybe with parents since they are so young. You can just buy a cake, order pizza... and all thats left really is fun for the kids... if you want to decorate you can, but they will be so busy swimming they probably wouldn't even notice anyway.
Good luck!
J.