Upvote:4
It takes about 50 minutes to get there and you have to change from subway to bus and then walk for a quarter of an hour. This wil cost you EUR 4.81 one way.
Muiden is too small a place to spend more than a couple of hours, so you'll probably want to return to Amsterdam.
Hiring a bicycle will cost you about 8 EURO. See http://www.amsterdam.info/transport/bike-rentals/ The bike ride will take about as much time as public transport.
Upvote:6
Just did this today, by bike, from Amsterdam City Center.
Go to the Flevopark on Amsterdam's impeccable bike lanes, then take the scenic bridge (Nesciobrug) and pedal for a few kms, mostly right along the river, in a park with bunnies (Diemerzeedijk / Waterkeringpad).
You'll cross farms, sheep, friendly people. Muiden itself has a few nice cafes and is sailing oriented. The castle itself is beautiful and smallish, and they close at 4:30pm, so try to get in at least an hour before that. Don't miss the garden outside.
Also right nearby is an old fort (Westbatterij) with cannons, behind which there's a very small and cozy beach, you can swim and enjoy.
This is the route: Centraal to Muiderslot by bike