here i have describe only three places where most people are visiting but there are many places to be visited. if any one intrested to visit as culture and history then anuradhapura, polonnaruwa ,dambulla, and kandy will be the main sights, then nature wise kandy , hortain plains, ella, beaches. as wild life people then wilpattu , minneriya or kawudulla, hortain plains, yala. birders, nuwaraeliya, hortain plains, yala , udawalawa, sinharaja and kitulgala are the best places to cover.
if we talk about sigiriya. its a world heritage site and unbelievable constructed site with in 18 years. about polonnaruwa it was a 12 a.d capital and you will able to see lot of monuments and artifacts.
minneriya is the most elephants gathering place in asia. once you do the safari or game drive you might ended up the tour with spotting over 300 elephants with in 2 hours.