Here's a few I've stayed in (other than the Hiltons):
Crown Resorts Henipa, Larnaka
Pretty run-down dingy hotel. A/c is mostly inop, no screen on sliding doors so don't go when it's hot. Small rooms, hard matresses (pretty typical, it seems). Very small bathroom with thin towels. Somewhat decent breakfast is its only saving grace.
Kapetanios, Lemosos
Beach hotel. Rooms in main building appear to be small. Had a room in the backing "executive" wing. Marble floors, quite large, but dark room. A/c worked very well. Efficiency with kitchen (not well equipped) with lots of counters, stove top, fridge + sink. Even came with an iron and ironing board. Food (dinner and breakfast) pretty appalling. Only reason to stay here (or Lemosos in particular) is proximity to Municipal Gardens (for the wine festival which is probably not worth going out of your way for).
Pendeli, Platres
Hotel in the hills high above Cyprus. Not too bad but rooms are pretty small. Front facing rooms have a great view down to Lemosos. No screens on sliding doors so beward during mosquito season. Breakfast isn't too bad Forest Park is supposed to be best in town.
At BostonBali's suggestion, I booked Kapetenios (and also Pendeli) through olympicholidays.co.uk
Some properties I didn't stay in but would like to try:
2 in Kakopetria
Maryland - "large" hotel built above a mill. Seems ot have lots of character (for a big hotel).
http://www.cymillhotel.com/
In the old town part of Kakopetria is the intriguing Linos Inn which occupies several old buildings.
http://www.linos-inn.com.cy/
In Lofou, the rooms attached to the Lofou Tavern (lots of character and a great place for a meze).
http://www.lofou-agrovino.com/
Lofou has the highest number (3) of taverns with character according to some Çypriot governmental organisation.