Hotel Joyce: 1912
The Hotel Joyce building has been at the corner of SW 11th and Stark since 1912. I wouldn't be surprised if the "Hotel Joyce" sign has been there that long too.
The "Fish Grotto" website claims they originated as Zack's Oyster House and have been "a Portland icon for the last 100 years." The current sign is not nearly that old but I wouldn't be surprised if it dates from the 1960s.
Check these out at the corner of SW 10th and Stark.