My wife and I and our two kids (boys 7 & 5) are spending a month in New Zealand in February and want to add a one-week stay at a beach to our itinerary. There are so many it is hard to pick. We want access to restaurants, etc. so not too isolated a location. Any recommendations? If you have any ideas on places to stay, that would also be helpful - our budget is pretty flexible but we will probably avoid top luxury places because of the long stay. We are visiting both islands so north or south are both options. Thanks.

Golden Bay perhaps?

http://www.goldenbay.net.nz/en/guide/pohara.html

Or Kaiteriteri?

http://www.kaiteri.co.nz/

I've never been there, but Hot Rock Beach always sounded interesting to me.

There are plenty of great beaches in NZ, so there's plenty of choice.
If you actually want to immerse yourselves in the water, then the North Island would be the best choice, but if you just want to play on the sand and dip your toes in, then there are plenty of nice places in the South Island also.
Have a look around Coromandel, or Gisbourne. Lots of lovely little settlements, with great swimming beaches. Wouldn't know about restaurants etc, but very few visitors starve in NZ, so I'm sure you would find something.
For picture postcard beauty, Kaiteretere, in the Nelson area is unbeatable, and it will probably be warm, too.