On a Sunday you should be able to find space in the surface lots oncommercial street near Christopher Columbus park. It will not be cheap.
If you get extra lucky, you might find a metered spot, which are free on Sunday. But do not count on it. Also read signs very carefully. A lot of parking there requires a resident sticker.
How close do you really need to be? You can park at the Post Office Square garage on Sunday for $9 and walk over. Or, you could park at the Haymarket garage, the one above the Boston Public Market, and walk over from there, which is the closest I think.
Post Office square isn't far. A little over a mile. Only $9 on the weekend.
There's a little lot on Cooper Street. $22 for 4 hours. Not the cheapest, but certainly convenient for restaurants.