Upvote:3
Anuradhapura is interesting if it's on your way (and it probably is). But do note that transportation in Sri Lanka takes a very long time per distance travelled. Whereas at home you might compute your average travel speed as 80 km/h, in Sri Lanka 20 km/h would be more realistic.
If you like trains, you should consider taking one from Colombo to Kandy (a famous route), and perhaps stop in Dambulla or Polonnaruwa. I would recommend spending a night wherever you decide to go, because it takes quite a bit of time to travel from Trincomalee to most other places.