The Barrelman and Jack-Tar for both beer and food. I give Jack-Tar a slight edge on draft selection and quality of food, but they're both good options and right in downtown/old town, respectively.
Three Cod Tavern on pleasant street has a nice tap list and an even more extensive bottle list. Sculpin, Newburyport pale ale to name a few. Was named best lunch in the region by readers choice awards and also best chowder. Say hi to Chip, the big guy with the mustache
If you go to Jack-Tar (my recommendation also) make sure to grab an app of their grilled wings. Some of the best chicken wings I've ever had. Shubie's on Atlantic Ave has a decent selection of bottles for purchase if that's your cup of tea too.
If you're up for going into Salem now that halloween is over, Gulu-Gulu and Flying Saucer both have excellent draft selections (and cans at Saucer)