The Sigiriya is not quite Anuradhapura, but it is the highlight of the country when it comes to historical attractions and nobody can visit Sri Lanka and leave without climbing up The Sigiriya Rock. If you plan well and head out early, you can climb the rock, climb back down and head back to your room for dinner.
If you want to cover most of the top places in and around Anuradhapura, the best thing to do would be to stay at one of the Anuradhapura luxury resorts the likes of Uga Ulagalla and travel to a site every day. If you dedicate a day each for the places that are about an hour or two away, you will be fine.