Hmmm. Jacob Wirth has some of the same 19th-century atmosphere, but it's far less glossy. The American side of the menu has some of that kind of food (I think the German side should be avoided), but it's essentially a tavern. A good beer bar, too.
McGreevy's in the Back Bay has the baseball-memorabilia overload of Caray's but more of an Irish-American pub kind of menu. It's also more of a TV-laden sports bar. I haven't tried the food here, but would have pretty modest expectations of it.
Eastern Standard might come closest to the overall big, casual but nice-looking old-timey ideal of those places, but with better food: it does French brasserie, American, and Italian dishes. It too draws baseball fans and tourists, mainly because of its proximity to Fenway Park. It's also one of the handful of 19th-century cocktail craft revivalists in town: really outstanding bartending.
You get that handsome old-timey pub kind of feel at Scollay Square (a re-creation, not authentic), but I've found the food to be just middling.