I've stayed at the Anemi Apts on a few occasions.
Simple, clean apartments and studios with friendly staff. Nice pool area with small restaurant area and a decent bar.
They are situated at the very top end of Bar Street and just around the corner from Bar Street. If you look at a map, the Annabelle Hotel is probably closest to these apartments but they are about 2 streets back from the seafront. Quiet location, never any night time disturbance and within 10 - 15 minutes walk from the harbour and fort area either by the seafront road or by cutting down Bar Street.
We got married from these apartments in 1999 in November. Evelyn, the lady who owns them gave me an extra room to get changed in so my husband to be didn't see me in my dress until I got to the Town Hall.
Sorry, I don't know really know the other accommodations but believe they are further out and heading towards Chlorakas/Coral Bay tourist areas (not Chlorakas village).
Winter time - most bars/restaurants will be open around Bar Street (Robin Hood bar is always popular), Tombs of the Kings road (near the King's Hotel location is more popular) and around the Harbour end of town. The other popular area at this time of year is by the Paphos Amathus Beach hotel, where there is an "island" of restaurants and small bars where the road splits.
Hope that helps a bit!
CwB