Farrell's (warning: link has annoying music) was my favorite, since I like ice cream more than I like pizza. Here's their history: The first one opened in 1963 in Oregon, but they were everywhere by the early 1970s, just as I was starting to have birthday parties.
It's supposed to look like an old-fashioned ice-cream parlor, with striped shirts on the employees and those goofy straw hats. The menu looked like a vintage newspaper and they had jars of penny candy.
The big treat, however, was The Zoo. It's like 40 scoops of ice cream (and a bunch of plastic animals, I think, which inspired the name?) and they bring it out on a stretcher with accompanying fanfare--sirens, drums, the staff running it out. I have no idea how much it cost when we were kids, but this blogger went to a Farrell's recently and it's $50!
You could certainly make a Zoo at home for a ton cheaper, but it's the experience, dammit. And Farrell's are expanding--they even have a Facebook fan page--so one might be coming to a mall near you. Rob and I laugh every time we go past what obviously was a Farrell's in L.A., and whoever bought it just turned the F into a B and renamed it "Barrell's.)
Shakey's was a big birthday party place, too. And they also had that turn-of-the-century feel, with banjo and employees in red striped shirts and hats. When we were kids, chain pizza places were a lot more rare than they are now, so going out for pizza was quite novel, and Shakey's party atmosphere made a lot of us grow up associating pizza with parties.
There are apparently 400 Shakey's globally, but less than a quarter are in the U.S., or so saith Wikipedia. It's also interesting to me that Shakey's was named for the founder's malaria-caused nerve damage, which I guess made him shake.
Where did you go for your childhood parties, whether yours or a friend's?