I don't know how else to say this, so here it goes:
I don't understand why your neighbor would invite a 2-year old to an 8-year old's birthday? Unless you're really good friends, I hope it's not to rack up more gifts. (I'm sorry I know that was mean but it was my first thought in reading your post.)
8-year old kids whiz through that joint like bats out of hell, all hopped up on soda and cardboard pizza. The games and ball pit are sticky and not the most sanitary, and the bigger kids are jumping and hopping and running everywhere like little monkeys. When my oldest daughter was between 4 and 6 she thought it was a blast but my youngest (1 or 2 at the time) was miserable. She was too little and fragile for me to let her walk around freely without being mowed over, and there wasn't very much for her to do. Oh - and the Chuck E Mouse that walks around? My kids are STILL petrified to this day.
It's always loud and crazy in there and most of the parents just let the kids do whatever they want. But don't get me wrong, it is a fun time for the older kids, and I know it costs the hosting parent's a decent amount of money, so I don't mean to completely bash it. It's just never been my cup of tea.
Frankly, I would hold off on Chuck E Cheese as long as you can! I'm sure you'll have many more invites in the future to look forward to. Send a gift down to their house and skip the party.
Also, in the future - I think parent's hosting the party expect you to stay when you have a toddler. I think a good age to drop your kids off at a party like that is age 5.