Hopefully you're a big enough fan to remember the opening credits, because they contain the only locations you'll be able to find. The rest of the show (including, unfortunately, the Regal Beagle) was filmed on studio sets.
There is one significant piece of good news, though: Diligent Internet nerds have, only recently, found the actual apartment building that served as the (external) set of "Three's Company." Given that the show's entire premise was the hijinks that ensue when a straight, single man shares an apartment with two straight, single women, the apartment is arguably the most important location.
The building, discovered by film-location blogger Lindsay Blake of IAmNotAStalker.com, is at 2912 4th St. in Santa Monica. Apparently knowledge of the location had been lost for a long time -- even Chris Mann, author of a book about the show (called "Come and Knock on Our Door," released in 1998), could never find it.
There are a couple of other locations from the intro that can still be found as well. The boardwalk scenes along the beach were shot at nearby Venice Beach, and the scenes of them goofing around on bumper cars and buying T-shirts together were filmed at the Santa Monica Pier.
You also have the opportunity to do a little research of your own. As I said, the Regal Beagle set was built on a studio lot in Hollywood, but various sources say it was inspired by one of two different Santa Monica bars, Chez Jay or Ye Olde King's Head. There are cases to be made for both, and both are within sight of the Pier, and just a few blocks away from 4th Avenue, so you can easily visit and come to your own conclusions.
Have a question? Email us at email@example.com. Please include your name and town. Personal replies will not be provided.