Hi Yogakshi, You should definitely visit Anuradhapura/Pollonaruwa, Sigiriya, Dambulla, Kandi, Nuwara Eliya, Ella, Tissamaharama, Yala, Mirissa, Koggala, Bentota, Hiriketiya and at last spend some time in exploring the city in Colombo
Below are a few places you can visit- Colombo - capital city
Galle - Fort
Unawatuna - beach
Mirissa - beach
Udawalawe National Park
Ella - Tea Plantations
Nuwara Eliya- Trekking and a place to see Hanuman footprints
Kandy - old city with beautiful architecture
Dambulla - rock cave temple
Sigiriya - rock fortress
Polanuruwa - Ancient Ruins
Hi, would suggest you visit a beach town... may be Hikkaduwa or Unawatuna... you may also cover Galle fort. In my opinion, Kandy is a waste of time and so are the national parks. Also, there is a small town, Ella, which is very popular among the backpackers, it has only one street and very limited stay options but cute little peaceful town... must visit cafe would be Cafe Chill at Ella. If you are interested in trekking, you may include Nuwara Eliya in the list and cover Horton Plains National Park, it's more of a trail though, a nice one. Please don't try to cover too many places as it would ruin all the fun.
Have a great trip !