Hi Marybeth.
In Cambridge area - if you are a sushi lover than I cannot recommend Cafe Sushi enough. Go with the omakase or order off the blackboard. Fantastic fish. Sarma in Somerville is a kind of middle eastern/turkish small plates place that has a lively bar and would be great for solo dining. Cafe Art Science is awesome for cocktails and the food is very good as well. Another good place to eat at the bar. Area Four in Cambridge has terrific pizza. State Park in Cambridge is a totally fun "dive bar" by the folks who had the excellent Hungry Mother. Fun takes on bar food, excellent cocktail program and fun bloody marys (pickled ramps and the like) as well as pool tables and shuffleboard. Alden and Harlow, again in Cambridge, is super popular (secret burger early in the night). It is a little heavy for my taste but people love it.
On the other side of the river - O Ya if you are a sushi lover is out of this world. Call soon for a reservation if you are interested. We love Pastoral in Fort Point for pizza and wood fired vegetables. Picco has great pizza and ice cream but has an ice cream ambience (lots of strollers) where as Pastoral has more of a adult ambience. Coppa in the South End is modern Italian with terrific homemade pasta, pizzas and great small plates. Lovely to sit outside on a nice afternoon. Select Oyster Bar (mentioned by Mike) is my favorite of all the oysters bars (Neptune, B&G, Row 34, Island Creek) - more inventive/former chef at Neptune. Uni in Back Bay is awesome. It took over the old Clio space and is world-inspired (for lack of a better description) small plates with a great cocktail program (sensing a theme here - this is a drinking town
). +! on Mamma Maria. We had a wonderful dinner there with A+P, Mike, Wendi, Lena, Kevin, Kate and Rosemary. Food was spot on (and the company was pretty awesome!) For a change of scene - you might enjoy a walk up the Greenway to the Boston Public Market - all local vendors.
For your Fenway concert, I second Island Creek (or its sister restaurant Eastern Standard). We camped out at Hawthorn Inn (a cocktail bar owned by the Island Creek/Es Standard people that is right next door) before the JayZ/JT concert at Fenway and it was a blast (Fenway is an amazing venue - esp. if you are on the field (even for a Yankees fan)). Chinatown after the concert (just saying) I would recommend Dumpling Cafe (soup dumplings are the bomb!) - it is a great late night spot (no ambience).
Legal - it has some of the best oysters in Boston in my opinion (the best we have had on a regular basis are out in Chestnut Hill - the oldest original location and we grab martinis and oysters at Long Wharf at the bar after a sail). I personally would pick other places for a meal (so many great places) just because so many of the locations are just choked with tourists. I cannot really speak to the food - we really only do oysters but the menu never really inspires me and is nowhere near as interesting imho as Select, Row 34, Neptune (tons of tourists here as well so we avoid) or Island Creek. But everyone is looking for something different. The reality is that the food scene has blown up in Boston certainly since I went to school here (20+ years ago - yikes!!) and gotten especially interesting in the last 3-5 years.
Breakfast - if you are at the Intercontinental you might like Flour in Fort Point which is not more than a 5 minute walk over the channel. South Street Diner (near South Station) is a popular place (Bob likes it - me not so much) but it has your typical diner food and has been around forever. Here is Boston magazine's take on breakfast in Boston -
http://www.bostonmagazine.com/restaurants/article/2016/01/31/best-breakfasts-boston/ If you are looking for great coffee - do try Sip in Post Office Square. Fantastic!