Family holiday in Denmark?

[warp9]

Hi. We're considering a family holiday (2 adults, 1 toddler) to Denmark, the first 2 weeks of September. However there are loads of cabins/holiday homes that all look good value, but I have absolutely no knowledge of where to go and what to do, other than a few days in Copenhagen. We'd prefer to be near the coast in a smaller town or village, with some touristy stuff nearby. I'm currently looking in the North Zealand area but am totally open to ideas.

Any suggestions?
Cheers