Unfortunately I didn't get the chance to see as much of Anuradhapura as I would've liked. I only had a few hours there as I was passing through and decided that it wasn't good value to but the entrance ticket. It cost US$25 and I thought it was pretty bad value. I do regret my decision now, for the record!
Regardless, there are quite a few sites you can see from the road and you won't need a ticket for. There are also a few smaller sites within the area that just cost a dollar or two to go into, so you can get a taste of the city without buying the full ticket.