Traveling Sri Lanka for 3 Weeks. What are Must Sees?

what   would  you like most ...  first you wanna  categorize

1. beach area  or hills or city and night entrainment

2. diving or food or history  or adventure .......

Must see: cultural triangle, Yala and the hill country

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 don't 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.

Thank you so much for all of the useful information!

your welcome!

Wow mal. You have covered so much about Sri Lanka in so few words. Very well done!

oddyearstravel - in addition to what mal has mentioned, may I also suggest you adding "Horton Plains" (also known as "World's End") to your itinerary when you visit Nuwara Eliya.

If you visit the national parks, you may also be able to catch a glimpse of a few leopards and bears. These animal are endemic to the country.

Do not miss walking along the ramparts of the Dutch Fort in Galle. I recommend this walk just before sunset. Pure bliss!

Though lots of people tend to just pass by Colombo on their way from and to the airport, may I suggest taking some time to visit the Museum, Independence Square, Old Race Course, Galle Face Green ... Also if you can, have dinner under the stars at Mount Lavinia Hotel. Do not forget to do some shopping when in Colombo.

Have fun and let us know how your trips goes.

Yes Farhaz, I forget many things. But the beauty of island can not be express in few words. In my case, still I am exploring new places inland.
How many ancient kingdoms in Sri Lanka? We can not forget, panduwasnuwara, Yapahuwa! And what about Gadaladeniya, Lankathilake, Ambekke ancient temples? We must not forget Kothduwa not very far from Colombo. Madu ganga is another interesting point!