well i took all my family to Benal for xmas and new year 05-06,and the weather was nice ,about 17-19deg in evenings ,it was a bit windy,and around 25deg in day.we stayed in my apartment,but it was nice to go to the shops xmas eve.they celebrate more on the 6th Jan 3 kings,and of course new year.i hope that is a start for you

Nerja is a good place to be. All the restaurants and bars will be open and everywhere is very child friendly.
Restaurants tend to have a special menu which can be quite expensive especially if you are feeding a number of kids! We usually take our family to a Chinese restaurant that is very reasonable and has a good part atmosphere with party bags and gifts. They also supply (as do most restaurants) the obligatory 12 grapes that are traditionally swallowed, for luck as the clock chimes midnight. ( Tip, take the pips out first.) The restaurants tend to be very busy so it would be well worth booking in advance.
There is always an open air party on the Balcon de Europa with fireworks and music. There are plenty bars but many people take their own champagne and party all night.
Nerja generally has very good weather at that time of year. My husband always takes our kids skiing while I stay at home and get a start on my year's suntan! The beach is possible if the sun is shining but it can't be guaranteed.
For apartments try looking at some of the listing sites such as holidayletting.com and rentin spain.co.uk.