We've stayed there a few times and liked it simply because it is away from the tourist area and very peaceful at night, We've always found the service there good - even now, years later (we live in Cyprus now and haven't stayed at the Agapinor for 4 or 5 years) we're greeted like old friends if we pop in for a coffee. It's busy round there during the day - the Market (full of tourist rip-off tat) is only 10 mins walk away, but quiet after about 5pm. A hire car is a good idea wherever you stay in Cyprus; the Agapinor has a reasonably big private car park and we've never failed to get a space in it.
If you're on half-board or B&B, might I suggest you stroll round to the Laona for lunch; Chris and Koulla (I don't know why they call her "Soulla" in the review below!) will welcome you like a member of the family and you'll get some of the best traditional home cooking in Cyprus.
http://www.cyprus-travel-secrets.com/cyprus-re staurants-laona.html