Much of Brookline is on the B, C, or D branches of the Green Line. Much of Brookline is a good distance away from the Green Line, too.
1) there's an IHOP and a whole lot of coffee shops (the usual chains and independents). There's also Zoe's diner (a bit further away) that I know used to be good but no idea recently. No great discount shopping in that area, but check out the Harvard Coop while you're in the Square.
2) Yvonne's is old fashioned. It's going to have atmosphere, but it isn't known for it's food.
3) Harvard level basketball is active and technically it is NCAA basketball, but it's not like what you might see on TV with the big hoops schools.
4) The "real" Cheers Bar (where they filmed the exterior) looks nothing like the TV version on the inside. It's a good place to get a T-shirt or a branded shot glass, not much of a place for a pint. The Cheers at Faneuil Hall looks like the TV one, complete with stuffed figures of characters and more tourists than you could imagine.