Train 91, The Silver Star, goes to Tampa
from NYC, Philly, Balt., DC, Richmond and points south.
Bus connection to St. Pete and Pinellas Park.
The schedule is here:
http://www.amtrak.com/timetable/oct04/T04.pdf
I think the train only goes to Orlando. I just asked a travel agent about that, but I will call Amtrak directly.