The ancient city of Anuradhapura was first settled ca. 900 B.C., and served off and on as the capital of the Sinhalese Kingdom until ca. 1100 A.D., when the capital moved further south. The city was quite large in its heyday, and so there is a lot of archaeology to see.
A $25 USD ticket will get you day admission to all the sites of Anuradhapura itself, and admission is included in the Cultural Triangle ticket$50 USD. Tickets can be purchased at the Archaeology Museum. Alternatively, most tuk-tuk drivers can get you in without paying the ticket. Some of them offer to take you in and tour you around for a price lesser than the price of the ticket. Decide for yourself between supporting local economy or supporting maintenance of historical monuments.