Boston's theater scene has an interesting split: the grand old houses that host the touring productions, and the scrappier developmental rooms in Cambridge and the Theater District where the stuff worth watching gets made first. Both are worth your time.
The Gold-Leaf Houses
Boston Opera House on Washington Street is the first stop if you want Broadway in Boston. Over 2,600 seats, a gold-leaf ceiling that makes you feel like you wandered into a palace, and an ornate proscenium designed in an era when theaters were cathedrals. Get dress circle seats for the view - you'll miss that ceiling from the orchestra.
Emerson Colonial Theatre has been running since 1900 and it has a specific thing going on: it's been a pre-Broadway tryout house for over a hundred years. When something new is in previews here, the buzz is real and the tickets are usually still available. The building is landmarked, the interior is over-the-top beautiful, and the Boylston Street location puts you two blocks from the best post-show bar options in the Theater District.
Where the Good Stuff Gets Made
American Repertory Theater up in Harvard Square developed Hadestown and Waitress before Broadway got them - both shows you've definitely heard of. The ART takes risks. Some nights you see something extraordinary; some nights you see something still being figured out. Either way it's more interesting than a road tour. Take the Red Line to Harvard, eat at Harvest or Alden & Harlow before the show, and make a night of the neighborhood.
The Laugh Rooms
Laugh Boston in the Westin Waterfront is the cleanest room in the city - comfortable seats, good sightlines, national headliners on weekends. The two-drink minimum is what it is. The Seaport Hotel bar is nicer than the in-room option anyway.
The stand-up scene at smaller clubs in Allston and Cambridge is worth exploring if you like getting in early on someone good - Thursday nights in a handful of rooms are where the future of Boston comedy is doing their tight fifteen. Check Evil Tickets when a touring headliner you want is landing at Colonial or Opera House.