Your best bet is to park in a nearby lot or even park a bit away and take the MBTA if you're dead set on going here or have an event/Meetup here. Street Parking in Back Bay is generally metered or by permit only.
There's a carpark opposite, but Dillon's itself is on a busy city street.
Not on site, but in the vicinity there's street and lot parking
Street only probably
Thanks! Your answer is awaiting moderation.