Anuradhapura is covered by the cultural triangle ticket (unfortunately not all notable sites within it), otherwise it’s a mere >$15 entrance fee. Some visitors are said to roam freely as the area is large and not guarded but as soon as you reach the Samadhi Buddha you’ll be more or less forced to do by the police (in a gentle way)
Anuradhapura’s archaelogical site is big and for the enthusiasts that want to visit every single monument, this may require several days visit. Nevertheless for regular visitors it’s certainly at least half day visit, requiring you have your tuk tuk to move you around.
Paying separate entrance for Anuradhapura may add a lot in your budget (around $15 !!), so it is wise enough and a good value to get the rather expensive (by Sri Lankan standards) Cultural Triangle ticket.
This cost around 40$ (!!) and covers six sights (Anuradhapura, Sigirirya, Polonnaruwa, Nalanda, Medirigiriya, Ritigala BUT NOT Dambulla caves and certainly NOT the temple of the tooth in Kandy.
The ticket is valid for 14 days from the date of first use and within 3 months of purchase. Unfortunately (again) it is valid for a single and NOT multiple entries in one sight.