Boston area street parking

I have to drop at a produce distributor in the Bunker Hill industrial Park Sunday morn, and rather than leave the city after del, I would like to walk around, maybe catch public transport into Boston CBD. The problem is I've been told not to stay at the distributor or park on the street. One recommendation is to drive to the Chelsea Produce market, show security my BOLs, and pay the market fee just to park. Besides the $20 market fee, I have to pay a bridge toll, I believe, making this one day adventure that much more expensive. Anyone familiar with the area able to recomend a close in and relatively safe place to park?