There is more than one station in Boston have you got a particular station you want to go from? Also generally off peak times are the best times to go to save money so usually mid morning to early-mid afternoon before and after school/work hours. Also not as crowded.
You will want to go to the Amtrak Tickets Site for all fare information.
A one-way from South Station, Boston, MA to Saint Paul (capital of Minneapolis) starts at $133, booked three weeks in advance. There doesn't seem to be any price variation on time of day or day of week.
A one-way from South Station, Boston, MA to Saint Paul (capital of Minneapolis) starts at $133, booked three weeks in advance. There doesn't seem to be any price variation on time of day or day of week.