Amsterdam's centre is fairly small, and almost abnormally flat, so you can easily get to most tourist destinations on foot - from the train station, within a half an hour.
A pleasant way to cover a lot of ground is to rent a bicycle. There are approximately three-quarters of a million people living in Amsterdam and they own about 600,000 bicycles. The city is very, very bike-friendly, and there are separate bike lanes on most major streets. In the city centre, however, there is often not enough space for a bike lane, so cars and cyclists share narrow streets. Cyclists have the right of way. If you are not used to that, be very careful, and also watch out for other cyclists. Avoid getting your tire in the tram rails; it's a nasty fall. Always cross tram rails at an angle. There are bike rental shops at stations, and several others in and around the city centre. Bikes cost about € 9 to € 20 per day.
A good map for cycling (routes, repairs, rentals + also public transport) is Amsterdam op de fiets (a Cito-plan). When preparing a route, there's a digital bicycle route-planner for Amsterdam, see Routecraft.com (http://www.routecraft.com/rlfplanneren)
Make sure to get a good lock, and to use it. Amsterdam has one of the highest bicycle theft rates in the world. Note also that if buying a bike, prices that seem too good to be true are stolen bikes. Any bike offered for sale to passers-by, on the street, is certainly stolen. There's an old Amsterdam joke: If to a large group of bicycles going by, you yell out, "Hey, that's my bike!" about five people will jump off "their" bikes and start running.
- MacBike Bicycle Rental (http://www.macbike.nl) Perhaps the most ubiquitous bicycle rental agency in Amsterdam, their bicycles are painted red with a MacBike sign on the front, everyone will know you're visiting. The bicycles are reliable, and in very good condition. Several locations around the city centre for assistance or repairs. Online bicycle reservations at their website.
- Orangebike, Rentals & Tours. (http://www.orangebike.nl) Their bikes are not so obvious coloured, more discrete, reliable and sturdy. Even the typical Dutch Grandmother bikes are available at Orangebike. Every day you could go on the 3 hour historical city tour and discover the hidden treasures by bike for €19.50 only. Online reservations on their website.
- Frederic Bike, insurance, bags, locks, and children seats all included for €10 a day. Extremely close to central station. Bikes are offered "incognito", for the discerning guest who does not want to appear "touristy".
- Damstraat Offer daily to weekly rentals. Have promotions in place with several hotels for "discount tickets", ask at the front desk. €12.50 for the first 24 hours, insurance included. Offers repairs for your bike and new and used bike sales.
The bicycle is ideal for exploring the surrounding countryside. Within half an hour you're out of town. Go North, take the ferry across the IJ to Waterland. Or go South, into the Amsterdamse Bos (a giant park), or follow the river Amstel where Rembrandt worked. You can also take your bike on the metro (with a reduced fare ticket, see public transport - http://www.gvb.nl/english/travellers/tickets-and-fares/Pages/Dog.aspx) to end of line Gaasperplas, and cycle along rivers and windmills to old fortified towns like Weesp , Muiden and Naarden.
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