Nerax has a good list, but you'll want to doublecheck with the bar itself to make sure they actually have a cask running (Lord Hobo, for example, has not had a cask beer offering on many of my recent visits). http://www.nerax.org/home/cask-in-boston.html
Stoddard's near Downtown Crossing comes to mind. Not sure about their Monday hours or current line up though.
Redbones almost always has a cask beer available. And the NERAX twitter feed has regular updates about cask tappings in New England including Boston - https://mobile.twitter.com/NERAX/tweets
The most recent casks that I know about are Slumbrew Attic & Eaves at Redbones, and Mayflower Winter Oatmeal Stout at Bukowski's in Boston.
Lord Hobo does have three cask engines (hand pumps), but they don't regularly use all three of them. I've only rarely seen them pouring more than one cask beer at any given time. (And lately it's been rare to find even a single cask beer pouring. Maybe I've been unlucky?)
Same with Stoddard's, but there's usually one of the 3 or 4 on. A couple of weeks ago they had Rich and Dan's Rye IPA and Czernobog for $5/pour, but I believe that was driven by a harpoon cask event.
Thanks for mentioning the NERAX Twitter feed. I do what I can. It looks like Redbones now has Sixpoint Brownstone on cask, and Old. Magoun's Saloon has Heavy Seas Powder Monkey. Magoun's usually taps a fresh cask on Thursdays and Sundays. Also on Thursdays, Russell House Tavern and PARK Cambridge in Harvard Square usually tap new casks.
@gentlebubbles Thanks for keeping us updated with the NERAX tweets! I check it regularly. I just sampled the Brownstone cask (dry hopped w Nugget) at Redbones. Delish. I just realized the link I included above is broken. Here's the right link - https://twitter.com/nerax
I dont think its luck. They rarely ever have one. I dont think it sold well when they opened so I really only see it served for special events or something like that.