My wife and I spent a very enjoyable week at the King Jason in mid-February 2007 and would echo the comments made by others on this site.
The KJ is a medium sized, modern complex located in a residential district away from other hotels. Bar Street, the main area of pubs & restaurants, is a 10 minute stroll away, with the sea front a further 5 minutes away. Perfect if you like to be near to the main tourist area but want the privacy that comes with not actually being in the middle of it. However, if you like your appartment to be 20 metres across the road from the beach, the King Jason is probably not for you.
Facilities near to the hotel are good. Round the corner from the KJ is a local shop which describes itself as a supermarket but is more like a large corner shop. It has all the basics you'll need for your stay and at reasonable prices.
If you turn left out of the appartments and head 200 metres to the main road, there is a bar called the Full Moon which shows all the live football on Sky Sports. There's another little shop just beyond that and a further 100 metres on the opposite side of the road is a little bakery which is excellent. Try the olive bread or the spinach & feta pasties. Superb but get there early as its freshly baked each morning and popular with the locals.
The KJ itself has a little shop which is run by a Cypriot lady who has several English ex-pats helping out. It sells stamps, English daily papers, freshly baked bread, bottled water, milk and everything from local wine & beer to pot noodles! It is fractionally more expensive than the nearby shops but it is convenient.
The hotel is run by Andreas and Maria who speak excellent English and whose professionalism is only outdone by their friendliness. The staff are also very friendly and helpful and everyone speaks excellent or passable English. Watch out for the cleaning ladies though. They take their jobs very seriously and won't except that a room doesn't require servicing. Our room was one of the first on the morning rota and any plans I had for a lay in soon disappeared! Also, rooms at the front of the hotel can suffer from early morning noise as coaches arrive to pick up guests with early morning flights. Not a major problem unless you are a very light sleeper. Rooms at the back front onto the pool area.
The hotel has everything you might expect ie. restaurant, bar, large pool, kiddie pool, games room, etc. The restaurant offers breakfast for those on a b&b basis and also a full evening buffet for CYP£9.95. We ate in twice and its superb value. There is soup & bread followed by an extensive salad bar, then a choice of hot food. Then there are desserts and a cheese board, followed by a local brandy and the local strong wine, Commandaria, which is like a port or sherry. As its a buffet, you help yourself to what you want as many times as you like but pace yourself as its very filling! The bar is pleasant but more expensive than in the town itself.
The appartments have all the basic facilities including a hair dryer, iron & ironing board, micro wave, towels which are changed regularly, and plates, cutlery, etc.
As for Paphos itself, it has some very touristy areas with Macdonalds, Pizza Hut, cafes offering fish & chips and pubs offering "John Smiths just like home". If your idea of the perfect holiday is Blackpool but with sunshine, you'll find enough to keep you happy. If, like us, you want to explore a bit of the local culture, there is also plently to keep you happy, especially if you hire a car and venture away from Kato Paphos (driving is straightforward but Cypriot drivers are mad!).
The local food is excellent. My wife and I are vegetarians so I can't comment on the meat & fish dishes (although other guests we spoke to said they were excellent). However, Cyprus is excellent for veggies if you keep away from the tourist hotspots. The local diet is based around a large variety of the freshest fruit and vegetables with plenty of olives, tomatoes, capers, beetroot and green salad, supplemented by feta and grilled houlloumi cheese. A number of restaurants will also offer Meze which is the Cypriot equivalent to tapas. The best we found in Kato Pahpos was Georgia, on the corner of Constantias and Tefkrou Streets, which does a 16 course veggie meze to die for! Its also renouned for its meat and fish mezes as well.
Beer in Cyprus is nothing special. Carlsberg and Keo are the staples although Leon is a very nice alternative lager if you can find it. Leon tends to come in bottles. I mainly drank Keo which costs around CYP£1.60 a pint in local tavernas to CYP£1.90 in hotels and more touristy areas. This is approx. £1.80 to £2.20 a pint in UK sterling which makes it a little cheaper than UK prices.
If the beer is nothing to write home about, the local wine certainly is! There are many local wineries producing all kinds of styles of wine and its worth taking a trip to one of them if you can. The local wines are also reasonably priced, from CYP£2 to CYP£5 a bottle in the shops to around CYP£6-CYP£9 in restaurants.
So, enjoy your holiday.