Egmond aan Zee is a very small town but it is built for family vacations at the beach. Nearby is Bergen aan Zee which is very similar. Bergen itself is not far and while it is one of my favorite towns I don't know how it will be for toddlers. It can be described as an artist community with a lot of shops and cafes.
Alkmaar isn't far (less than 20 minutes) and is a great town to wander. The kids would probably like the cheese market on Friday morning but it can get crowded. There are a couple pedestrian only streets you should enjoy walking. If you have never had one be sure to get the kids a rookworst (think hot dog) at the Hema. Take the kids to the Molen van Piet. In my mind one of the most beautiful windmills in The Netherlands. Better yet take them to the Windmill Museum about 12 km outside Alkmaar at Schermerhorn.
A neat day trip might be to visit Hoorn and Enkhuizen. A wander along the harbor in Hoorn is delightful. Be sure to read up on its history and where it fit in with The Dutch East India Company. One of the best things you could do would be to take the kids to the Zuiderzee Museum in Enkhuizen.
As for biking I think you have chosen one of the best areas in The Netherlands. You'll find fietspads (bicycle paths) throughout the dunes and inside the dunes line. One of my favorite trips was always through the woods between Bergen and Bergen aan Zee. While I didn't look you should have no trouble finding a bicycle shop to rent bikes.
Just north of where you're staying is the Afsluitdijk. Built to enclose the old Zuiderzee it connects North Holland with Friesland. Drive across and take a wander through one of the maritime villages of Makkum or Harlingen.
https://www.zuiderzeemuseum.nl/en/10/home/
https://www.museummolen.nl/ Open in Google Chrome or use Google Translate.
https://www.kaasmarkt.nl/en/
https://www.holland.com/global/tourism/destinations/provinces/friesland/the-afsluitdijk.htm
"Not all those who wander are lost.” ― J.R.R. Tolkien
Edited: 6 years ago