OK, Showbiz and Chuck E. Cheese kinda came along after I was too old for a pizza parlor birthday. I was of the Farrell's and Shakey's era, you? Do you remember where your pals had their parties, and what you did? No video games in my memory of these parties, but I remember lots of LOUD LOUD LOUD ragtime music, not-so-hot pizza, and some enormous ice cream sundae thingamabobs.
Was it Farrell's that had the Zoo, with plastic animals on a gigantic sundae? Yes, according to this page. These folks visited a Farrell's in 2003, and watched a Zoo being made and delivered. It's 40 scoops of ice cream! And bells and sirens go off when it's served!
Here's an awesome 1974 commercial showing a Farrell's Zoo being delivered. It weighs 8.5 pounds!
But whichever birthday-party era you're from, don't miss this gaggingly poorly acted video where Showbiz Pizza tries to tell its staffers how to sell its parties.