Amsterdam is not a vast city. Within cycling half an hour or so, you’re in the countryside.
Nice day trips are possible north to Waterland, south along the Amstel river or south-east to the river Vecht and a couple of old fortified towns there (Weesp, Muiden, Naarden).

Weesp (10 miles from the centre of Amsterdam) is a good starting point. You can cycle there along the impressive Amsterdam-Rhine canal. Or take the train and rent bikes at the station in Weesp. It’s only 15 minutes by train from Amsterdam Central station to Weesp, four trains per hour.

Weesp is a quiet little town with a nice old centre (Gothic church and City Hall build 1776) and a couple of windmills.
In fortified Muiden (2 miles north of Weesp) the medieval castle Muiderslot can be visited.  To get to Muiden and the castle, just follow the bicycle signs from the Tourist office in Weesp that read "Muiden Route," which will take you straight to the castle.  The route is very safe with lovely scenic views of the Dutch coutryside along with way.  Naarden (5 miles east of Weesp) is one of the best preserved fortified towns in Europe. One of the forts is now a Fortress Museum.  The countryside between these towns is classical Dutch, with rivers and canals, cows and windmills. Great sightseeing.

Cycling is pretty safe here. Either there are separate bicycle paths, or narrow roads with limited traffic.
Anyway, you don’t have to cover large distances, as the sights are not far apart.
So, a cycling trip is also very well possible with children. They’ll love the castle and the forts anyway.

On this link page you can find a lot of practical advice and routes in this beautiful region just outside Amsterdam.