Have you already decided where to stay and what are your main interest of site-seeing??
Its a beautiful small country with a big bio diversity. It is green always.
If you like to view historical kingdoms, Anuradhapura or Pollonnaruwa, at least It may need full 2 days to cover each of the ancient cities. You can cover Kandy (famous for Buddha's tooth relic and the Royal Botanical garden) and Pinnawala (elephant orphanage) within a single day if you are traveling from Negombo/Colombo by a hired vehicle. Otherwise it is difficult by public transportation. Above Kandy is Nuwara-eliya famous for tea plantations and water falls. Whereever you look, you can see green tea bushes. You may need at least 3-5 to cover whole area of Pinnawala-Kandy-Nuwar eliya via Ella gap. Ella gap is a beautiful place where you will see sun rise.
On your way if you like to spend another day, you can go to Seegiriya Lion's rock and Dambulla Golden temple.
Pasikuda, Arugambay, Mirissa, area are well famous for nice beaches. If you dont like to go there you can travel to Galle and Matara in down South and spend few days.
There are so many national parks in Sri Lanka (around 21). You can see wild elephants, deers, crocodiles, wild boas, pea-cocks, jungle fowls (national bird of Sri Lanka) and various kinds of endemic and migrating birds. (Kumana is famous for birds)But you will have to select which national park you must go as the animals (mostly elephants) migrate one to another due to seasonal changes.
For Kandy temple, Pinnawala, national parks and cultural triangle, you will need to pay an entrance fee! Paying one time for Cultural Triangle ticket you can see whole the main archeological valued places- Polonnaruwa, Anuradhapura, Kandy, Seegiriya & Dambulla.
(When you enter into a temple, you cannot wear shoes or hats and when you go inside Kandy Temple,
you are warned not to wear shorts, short skirts and sleeveless outfits)
It is easy, comfortable and timesaving to travel by a hired vehicle but some back-packers use public transportation as preferred!
Have a nice trip and welcome to sri Lanka.