I think that two of the best cocktails bars in Boston are pretty close to you: Eastern Standard and The Hawthorne. ES is my favorite. Drink, which is in Fort Point (close to the old Trillium spot) is another popular cocktail bar, but I've never been.
If you're willing to cross the river, I would recommend Alden & Harlow in Harvard Square, Cambridge. I love their cocktails and their food is very good. Very easy to get to via public transit (red line to Harvard Sq.).
Lastly, I'd be premiss to not plug my favorite restaurant (anywhere, really), which is Sarma in Winter Hill, Somerville. Good cocktails, ok beer options, but phenomenal food ("modern mediterranean"). It will be hard/impossible to grab a reservation now, but if you show up 20 min before open the bar is first-come and you can eat there.
Let me know if you have any questions or if I can be helpful.
These are great! Thanks! Sarma looks right up our alley, but don't know if we'd be able to get there right at open