Sri Lanka is about 430 km from north to south, but roads are slow. Pick a few regions and give each time.
Regions
Colombo
The capital: markets, temples and good restaurants.
Cultural Triangle
Sigiriya, Dambulla, Anuradhapura and Polonnaruwa.
Kandy
Temples, a lake and the gateway to the hills.
Hill country
Nuwara Eliya, Ella and the tea estates.
South coast
Galle, Mirissa, Tangalle and Yala.
East coast
Trincomalee, Pasikudah and Arugam Bay.