Full disclosure: I am an acquaintance or friend of nearly everyone on the Happy Dog's front end. But even before I got to know the staff, I fell in love with this bar. I've never really been one to have a "regular" place because I've always valued anonymity, but there's definitely a cozy element to the Happy Dog that I haven't found anywhere else. The food is delicious (and cheap!), and the unique combinations on the menu make for some exciting choices. They also have a lot of premium beers on tap, including Scrimshaw, Mirror Pond Ale, and Fat Head's Bumbleberry.
9 times out of 10, the live music is an asset to the atmosphere. I've seldom seen bad performances at the Dog, and it's been a spot for a LOAD of great Cleveland bands. Monday Night Trivia is also enjoyable and has proven to be an effective way of decompressing after a stressful work day.
I highly recommend this place to locals AND tourists. There's no place on earth like it.
(P.S. The pinball machines should also get a mention. The Dog is a regular spot for the Cleveland Pinball League, so the games are satisfyingly challenging and they switch them out every so often. As of this writing, Attack From Mars is my favorite. I've spent many, many quarters in these machines and I certainly urge you to do the same.)