I’m a fan of the Dough sticky buns.
On my last visit to Boston in 2018, a fellow Chowhound/ FB friend/ pastry chef (!) based in New Hampshire mentioned Tatte Bakery’s morning buns and a few other pastries. It is a chain with several locations, but it’s much better than any chains and most bakeries/ pâtisseries in Toronto. It was a treat and I’m glad she mentioned it. There are some Tatte locations that are convenient to museums around town.
I kept my meal at Neptune very light because I had dinner plans later. I think a bowl of chowder and an appetizer mid afternoon. I really enjoyed it and I’m glad I went.
I also really enjoyed a hot lobster roll at Select.
I have stayed in Back Bay on my last 2 most recent visits (April 2013 and Oct 2018).
There is a Trader Joe’s nearby, in case you’re still based in Canada, and want to make a pit stop. 
