When we first moved up here, I had to stop and think about it as I always wanted to pronounce it pully-up. It’s PU-ell-up. Home of the WA State Fair - used to be the 6th largest state fair in the US, not sure if it still is or not but it’s YUGE.
Another one is Sequim - wanted to pronounce it see-qui-um, but it’s really squim.
Most people I know say Pee-ALL-up I’ve never heard it pronounced like you wrote. But you’re from Washington so I’ll defer :]
Two years ago my wife and I set up a large display with our close friend, Army Master Sergeant Mike Emmons honoring Vietnam Veterans. We were at the fairgrounds every day for over three weeks... if you include set-up and break-down.
Many of the items in the display were irreplaceable so someone had to be watching it from the time the fair opened up in the morning till the time it shut down late at night. We didn't lose anything important, but on several occasions kids made it past our stanchions and onto a very rare Vietnam era jeep. They would start indiscriminately shoving valuable artifacts off the jeep and onto the floor so they could sit in the seats. When we would chase them off their parents would protest and say that they just wanted to get a picture. In every case it was actually the parents who egged their kids on. We had 10,000 or more visitors visit our display pretty much every day accord to the fair employees. It wore us to a frazzle.
My wife and I both were born in the area and many people including some natives do say “PU-ell-up”, but that is usually when they are saying it fast or singing the fair theme “Do the Puyallup”. The pronunciation my wife and I were taught from the time we were little tykes growing up here, by our parents who also grew up here is PU-ahl-up.