The Downeaster uses North Station beneath TD Garden. The market, Greenway and Old State House are walkable from here. South Station and Back Bay are different stations and require a separate transfer.
Times to reach each place are planning allowances from the station, not measured routes. Check directions, opening hours and accessibility before you go.
The market documents a walk of under ten minutes from North Station; this allowance adds time for station access and crossings. Vendor availability and seating are separate.