Start you day tour at Independance square, can get a bit if our history there, then the independence arcade it's a shopping center which used to be the asylum during the colonial days.
Then walk on independence avenue to the museum (if that is something you like), then to Victoria park and enjoy the big park in town.
Then Gangarama Temple and the small island temple in the Beira lake close to the Gangarama. You will be tired by now so have a coffee or something and chill.
Then go to Pettah area, check out the Woverndhal Cathedral, the red mosque, Hindu lovely and temple.. also the Pettah market.
Then head to Grand Oriental Hotel a very old hotel with ALOTTTTT OF HISTORY. Go to the Harbor room and have ice tea, beer and enjoy the view of the sea at an elevated position and the entire Colombo harbour and port.
Then walk to Dutch Hospital (Pagoda Rooms is a good place to have a decently priced lunch). After the Dutch Hospital Halle face green ... Then Colpitty Market .. Then done.
At each if these places you have things like the last king of Sri Lanka final place of keep by the British to old Dutch, Portuguese building and the first entry gate to the old bells. Depends again what your interested in.