1. The idea of dividing the vacation into two parts: cognitive and beach, is very sound.
2. The central part of Sri Lanka is a region with interesting places: Kandy, Nuwara Eliya, Ella, Dambulla, Anuradhapura, Polonnaruwa, Sigiriya. It makes no sense to settle in one place, it is most reasonable to spend the night every time in the city where sightseeing is planned in the morning.
3. No need to flirt with "inexpensive housing" in Sri Lanka, this is not Thailand for you. It is better to overp ... Farther...