Spend a little time on the lakeside
Anuradhapura is surrounded by lakes - Nuwara Wewa, Tissa Wewa and Bussawak Kulama are the biggest of them. Lakesides are a perfect place to take a rest or make a picnic after visiting the Ancient City. It will give you a opportunity to meet the locals, to be invited for a grilled fish, or to buy one from a fisherman and to grill it by yourself...
Chill out in the shade after a day in the sun
The Royal Pleasure Gardens are not really off the beaten path but could easily be overlooked in the midst of so many impressive ruins.
The photo is of one of the many garden caretakers mowing the grass.