It's funny because I remember attending many out-of-house parties as a kid, and even had a few of my own (swimming, bowling and movies were common options) however, all the kids parties I've attended as a grown up (for friends' kids and nieces and nephews) have been at home, or in the case of one friend, at a park.
I helped my sister put on my 8 year old niece's party last summer at her house, and it was a blast: we did a carnival theme, involving a giant plinko game (made of cardboard and golf tees) "throw water balloons at Dad", Duck pond, pick a door (get a prize or squirted in the face with a water gun, depending on the door - made from a tri-fold cardboard display) and face painting/temporary tattoos. Snacks were homemade popcorn in paper bags, licorice, and lemonade. I doubt she spend more than $50, as it was all from the dollar store, including a roll of tickets that they used to "pay" for the games.
All the kids had a blast, it was cheap, the kids stayed outside, so house-damage was minimized, and it was fun to put together. Although, undeniably, it was a lot of work.
That being said, I don't have kids, so I don't really know what's common in wider circles. Maybe I just run with an unusually frugal bunch. Also, while my SIL always does parties at home, they always involve a bouncy castle, a custom made fancy-pants cake and usually an entertainer (reptile person, magician etc) so that's probably still pretty expensive, even though it's in her house.