There are some nice bars in the area around Taj tbh. Globe is right by there, and Beantown Pub isn't a far walk (other side of the common). Highball Lounge is over there too, but it's a different vibe (laid back, lots of board games, but expensive and sort of hipstery). If you want more of a sports bar scene, head a few blocks down Boylston and you get Whiskeys, Pour House, McGreevys, and Lir all next to each other. Lir is my favorite of that group, p chill spot. Could also go to one of the bars by Back Bay Station... Brownstone or Clerys. Both are good, but I think the food is better at Brownstone.
As far as lunch spots go, there are a ton of options in Back Bay, yeah. I have stated my love of Back Bay Sandwich many times, though that's weekday only I think. If you want Thai, House of Siam over on Tremont is one of my favorite restaurants in the city, and their lunch prices are p good. Something quicker is the burrito stand in Back Bay Station, Cha Cha Cha. They're legitimately really good, cash only though.
There are also a looooot of food trucks in that area, though again, most of those are probably better bets for weekdays. There are always 3 food trucks for lunch on the Trinity side of Back Bay Station, plus another down Boylston by the library, and another on the corner of Clarendon and Boylston. There's a schedule of the rotations online I'm sure you could find, but most of those trucks are solid.
edit: ooo I almost forgot, there's a really good pizza place on Newbury called Dirty Water Dough Co. Maybe a 10 minute walk from Taj. I've never had a bad slice there.