If you look around the web there are various maps to be found. For sc have a look at holiday rentals.co.uk.

The Kermia Beach is very pleasant. It's a few kms east of Ayia Napa and has lovely pool area and private beach. I know that Olympic and Amathus do the Kermia. It's very quiet, as the complex is secluded.

Kermia have a great reputation and are in a lovely location situated on a hill top outside napa on the protaras road
here is their web page take a look and let me know what you think
http://www.kermiahotels.com.cy/

The Andreotis apartments are just on the edge of protaras and are very nice, we stayed there last year.(Thomas Cook/Sunset I think)They are within easy walking distance from the main strip with the bars restaurants etc.
Why not consider Ayia napa???
It really is a lovely place with lots to do and see ,but not rowdy like you imagine ,there is someone for everyone,all ages.
Please don't dismiss it if you have never been,we prefer it to Protaras(which has too many Elvis impersonators and Karaoke bars!!)
Good luck!

Oh my! Kermia is soooooooo expensive... you could get a 2-bed apartment for two days' rent of their 2-bed bungalows.

Marion

Thank you all for replies. Unfortunately this is an unplanned holiday - have to go elsewhere later - so budget is a bit tighter than normal but would like reasonably good cooking facilities in clean quieter area- any more ideas welcomed - cheers!

Try the Andreotis as already suggested - we alsostayed there lst year and the location was ideal - out of the main town but walkable. Also on the main road out to Ayia Napa. (don't worry - we dodn;t find the road to be busy) We asked for a pool view and got a lovely apartment in one of the bungalows. Perfect. Where ever you end up I wish I was having an unplanned holiday to Cyprus - you will love it and maybe next time Cyprus will be your frst choice destination.

brilliant apartments!this is a lovely accomadation wiv a lovly pool!got entertainment in the evening and it is about a 5 minute walk so you are really in the midle of evrything but you will not here any of the entertainment from in resort!

Stayed at The Brilliant Apartments also - these are in a great location too. Away from all the noise but close enought to zig zg home at the end of a lovely evening. Rooms were quite large and clean.