I have been to Cyprus 4 times as my sister lives there and I think it is a wonderful country. The weather is always brilliant, but very hot mid-summer, I would recommend going in October or in May when it is about 27-30 celcius.
The locals are very friendly and the majority speak english. In one hotel we stayed they had no high chair so for the first few days the waitress would take my baby for a look around the restaurant while we had breakfast and on the third day they had bought a new chair for us, very kind.
I have stayed in Paphos, Aiya Napa, Nicossia and Larnaka. Larnaka is my favourite place to stay. It is close to Larnaka Airport. Because of Larnaka's location it is a good base to explore the rest of the Island and I would recommend hiring a car and visiting the ghost city of Famagusta, which the Cypriots had to flee from in the 1970's when Turkey invaded the Island. It is now a no-mans land but can be viewed from a village called dherynia. Also the divided city of Nicossia is worth a visit, one side is greek cypriot and the other is turkish. Nicossia is a very cosmopolitan city so head there for shops, restaurants and culture.
Larnaka is on the coast, as are all the tourist resorts, but it also has a lovely Marina. All along the marina there are hotels and restaurants with outside, shaded eating areas.
We stayed in the Sun Hall Hotel which is on the front and has wonderful views of the sea and beech. It is a few seconds walk to the beech and the marina, so a great location. They serve a great breakfast with a large buffet to choose from and the rooms were very nice.
There are some lovely boats on the marina, some of which do day excursions. The one we took was a glass bottom boat which was £2 cyp each for about an hours trip to see an old boat wreckage, the view from the glass bottom wasn't very clear but it was a nice trip.
Behind the marina there are many shops. Not just the tourist shops but shops like Mango, Zara and U2 along with department stores. The prices are cheaper than the UK and it is also different stock. You will also find more restaurants and bars here.
It is a quiet resort. There is no water park and other than the beech and hotel pools I wouldn't say there is much for small kids. I would recommend it for Couples or anyone without small kids. However, Aiya Napa is only half an hour away and it does have a water park and amusements so great for a day out.
It is cheaper than Paphos or Aiya Napa for eating out. In 2002 there was 3 adults and 2 teenagers and a baby, who didn't eat, in our party and our usual cost for lunch in a marina cafe was approx. £13 cyp which at the time was about £16 stg. Our lunch was usually club sandwiches and salad and a cold drink. Restaurants run by the locals are nearly always the cheapest as is anything which is made or grown on the Island, such as seafood, bread, Keo beer, fruit, etc.
So, overall I would highly recommend larnaka and Cyprus as a holiday destination.