Cocktails within walking distance of BPL?
re: babka eater
And if you want one of those crazy long cocktail menus, City Bar is a block away (and City Table). Across the street is the Charlesmark which has a nice little lounge area (don't really know their drinks). In the Westin is Bar Ten which is pretty good, I liked their flatbreads.
Cocktails in the Back Bay can be expensive and not always great at the price. Here are a few ideas.
Nice hotel bars: Bar 10 (Westin), City Bar (Lenox), Oak Bar (Fairmont Copley), Sel de la Terre (Mandarin Oriental), Salon at L'Espalier (a lounge, not a bar, but superb cocktails and snacks, Mandarin Oriental), Brasserie Jo (Colonnade).
Luxury steakhouses (reliable bartending, if pricey): Morton's, Abe & Louie's, Grill 23 (has one of my favorite bartenders).
Newbury Street (carries a tourist premium, better if you can sit on the patio): Bouchee (Epcot Center French food), Tapeo (beer/wine only, but good sangria), Sonsie (sit in the cafe area up front), Pazzo.
Other kinda-fancy Back Bay restaurants: Douzo, Via Matta, Post 390 (which I actually don't like for food or cocktails, but the atmosphere is great).
Back Bay casual: Bukowski (the beer lover's choice, with cheap, okay food), Parish Cafe (pubby and pleasant, with a good beer selection), Rattlesnake (not outstanding for drinks, but the food is much better these days).
Walkable in the South End: Coda (a good value in this bunch), Delux Cafe (surprisingly good drinks for a bar with a younger crowd, decent inexpensive food), Petit Robert Bistro (tiny, pleasant bar, very nice French food at real-bistro prices), Anchovies (dark, cheap neighborhood bar with decent Italian-American food).
My favorite lately is Legals at Copley between 4-7 weekdays. With cocktail purchase at the bar, they have an excellent deal: $1 oysters (any kind from Wellfleets to Kumamotos, and they are fantastic), plus $3 appetizer menu including mini smoked salmon sandwiches and coriander-encrusted tuna sashimi. I usually get those, plus a couple of sides from the regular menu: broccoli with cheese, and polenta, or seaweed salad. If you check it out, I advise against the spinach-feta dip off the $3 menu, but I love the rest of it.