The rather charmingly quaint Semeli is a great alternative to Nicosia's larger top-end options. Classically styled rooms have wood floors and balconies; there's a bar and a restaurant, and helpful staff. It's extremely popular with groups, so fills up fast. Booking in advance can get you €10 off the rack rate.
It's a bit of a hike from the Old City, on a quiet side street just off Leoforos John Kennedy.