Wow, what a range of advice!
Personally, we have a very tiny house and even having two additional families over is not very comfortable--add toddlers to the mix... oh boy! Plus, it's a lot of work to get the house party-ready, only to have to clean it up once more after the party. I can totally relate to wanting to do it elsewhere. After our older daughter's 2nd birthday party, my husband and I agree that it's "out of the house" until they're old enough to appreciate sleepovers, OR we get a bigger house ;)
We have been to two parties at Pump It Up with our "almost" 3 year old and she had a BLAST both times (so did my husband)! They are for ages 2 and up, but it sounds like that won't be an issue. We are having her 3rd birthday party "back home" at one of the franchises with her cousin, and many family friends with kids (mostly under 10). I also like the idea of a "time constraint" since you only get X amount of time for the party arenas, and then X amount of time for the party room. Have you been? they do offer "toddler time" drop-in sessions in the mornings during the week usually, I think it's $6 a kid or something for an hour or so. You can check it out and see if they like it.
We also LOVE the Imagine Childrens Museum in Everett! We have a membership and have considered a party there as well. I think if the majority of the kid guests are 10 and younger, they'd have fun there.
There's always Chuck E Cheese ;o) Nothing says "birthday party" more than losing your hearing, eating bad pizza, and getting bumpted/run into by toddlers, kids, teens, etc. for hours! Of course, if you ask our soon-to-be 3 year old, that's where we're having her party!