If you have time, go to Bully Boy Distillery (a short Uber ride) or Short Path Distillery (in nearby Everett, also a short Uber). Both are in industrial areas. Bully Boy is the better tasting room, but the beauty of Short Path is that it's right near Bone Up Brewery & Night Shift Brewery - and good for a night out. Short Path also makes gin & other stuff.

Otherwise, I really like Saloon (they have 120+ whiskeys) in Davis Square off the Red Line. It's a quintessential whiskey bar and has pretty decent grub too.
The Quiet Few in East Boston has a great selection, it's my local spot. It's a short walk from Maverick Station off the Blue Line, about 6-7 minutes commute from downtown. I like their burgers. Great staff. Though it's tiny and can get crowded.
Worden Hall in South Boston is solid.

If you have to be downtown, The Last Hurrah is the hotel bar for the Omni Parker House and is pretty iconic.

In the Fenway area, there's Citizens Public House. Food and cocktails are okay, though they have a damn good selection. Also - pickleback shots on draft. But if you're going there, I'd highly recommend going to Fool's Errand across-ish the street, which is a tiny standing-room (mostly) craft cocktail bar.