Oh fun times. The thing about Boston is I feel most places have a casual vibe but will still wind up being fairly spendy because Boston remains a pioneer in the lands of $7 beer. So I’ll give suggestions based on what I know has really good food and good booze and then you can check out websites and sort it into your budget. :)
Okay — for interesting menus I’d go with —
Toro — tapas in the South End. Food is amazing. They don’t do reservations, there will likely be a line, but seriously, if you go get the corn and be unafraid to make a mess.
Tiger Mama — Asian fusion in the Fenway neighborhood. If you go and you like pork, get the pork rice. Sister restaurant is Sweet Cheeks and it’s on the same block. Really solid southern food.
Shojo — on the border of Chinatown. Asian fusion, super good.
Tremont 647 — Super good and inventive American
Pizza — Picco in the South End or Ernestos in the North End (get it to go and eat on the greenway)
North End for italian, obviously. I like Lo Conte for old school italian. You’ll get giant plates of pasta and it will taste good. It’s not terrifically adventurous, just solid. Other than that, any restaurant at the start of either Salem or Hanover streets will be uniformly excellent and roughly the same price. Fiore on Hanover St has a nice roof top bar area.
Ice cream — JP licks
Brunch — North St Grille in the North End. I think they might even do reservations now. Stephanies on Newbury. Crossroads for solid and unpretentious, yet tasty. It is a soccer bar (Man United mostly), so it can get crowded. Also there’s the Paramount on Charles St in Beacon Hill. Don’t be afraid if it looks like there is nowhere to sit. It always seems to work out.
General grab breakfast/coffee/pastry — I’d suggest checking out Flour. There's one just behind the Back Bay T Station. There’s also a Tatte on Charles St in Beacon Hill now.
I am useless when it comes to shellfish (allergy) and sushi (husband deeply dislikes, so we never eat it).
For really good drinks —
Eastern Standard — right near the Kenmore T stop. If you like cocktails, would suggest popping in before/after the Sox game. Food is spendy but excellent.
Drink — Seaport. You tell them what you like, they create drinks for you.
Lower Depths — near Fenway. Food is good and the beer list is massive. Good for before/after the game if you can get in and you like beer.