The northern Sri Lanka city of Polonnaruwa is most famous because it was the capital from the XI to the XIII centuries. Some of the ruins are now part of a UNESCO world heritage site. To get there, there are a few direct buses from Kandy, or you can take any bus heading north, changing in Habanara. The buses are not air-conditioned, and some go directly to Anhuradapura to reach the old capitals. There are a half dozen low-budget hostels. We stayed in the Manel, which is fine, but all are worth it. You can stay for 5-10 euros in a clean and decent place. Polonnaruwa is next to a lake, we were there in the dry season and we didn't feel like swimming. The new city, which is mostly tourist oriented, has been built next to the ruins. Most people understand some English.
In Anuradhapura (the holy city) there is a complex of temples, stupas and other buildings that are perfectly preserved with the incentive that they are "alive." Several times a day religious people go to gather and give all kinds of offerings and hold ceremonies.
Colombo is the capital of Sri Lanka, and this is where most travelers come to visit. It's a culture shock, everything moves quicky, it is loud, it is difficult to locate, the city is huge. The town is 30 kilometers from the airport, and there is a free bus to the central bus station. But then the natives see your face and they try to offer tourist buses, taxis, guide services, hotels , etc. The city has a nice colonial center, but with the new civil war, it was dubbed a "high security zone" and difficult to reach. Other than that, to have a quiet arrival, I recommend that you spend the 1st night on the beach of Negombo, 10 km from the airport. Colombo is used as a transit point for bus or train to the beaches of the South and Kandy. The city has nice neighborhoods that are to the east and are named cinnamon gardens.