First time to Amsterdam, and really can't afford to spend a lot on activities. I've heard the museums are great...are any of them free? I love the outdoors, being active, etc. and would really like to explore as much of the city as possible on the cheap!
Like Tiffany said, a good way to explore the city is just walking, which is of course entirely free :-).
If the weather is nice try the app "We're on a Boat". This is an app whereby locals can offer a free spot on their boat to people who are interested. The 'captain' might ask for you just to buy some drinks or a small fee for gas (or nothing). So a lot cheaper and much more fun than your standrad canal cruise boats.
A cheap restaurant is Buuf eten. Good meals for €8,50 and a good 'at your grandmothers home' atmosphere.
Depending on when you are going, just go to one of the parks like Vondelpark to people watch. Buy some food at the local supermarket (for example Albert Heijn) and just have your meal in the park.
If you are here in a Sunday try to see if there are local markets like Pure Markt or Sunday Market. You don't even need to buy anything to have a good time. It is already nice just to look what all the different craftsmen are offering.
I don't know any free museums in Amsterdam, sorry.
My favorite thing about Amsterdam is just walking. It's a beautiful city to explore by foot with many shops, beautiful buildings, canals and bridges, and old churches to explore. You can spend quite a bit of time enjoying it by foot. Talk to locals. They all speak English extremely well and are generally friendly.
The museums are not free. The Rijksmuseum Amsterdam, for example, is 17.50 Euros for admission, so if you're on a tight budget, either pick the one or two important ones (I also love the Van Gogh Museum and the Anne Frank House is very special), OR, if you can afford it, try one of the following passes. They are each slightly different in what they offer. I think the second two are actually a much better deal, but check out the links. The passes will save you time because you can skip the long entry lines to the more popular attractions and they'll save you a ton of money.
There are tons of little cafes with inexpensive food - "broodje" is a sandwich. You'll see that on menu's often.
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Most activities does cost money in Amsterdam, so it's difficult, but i got some tips for you.
Markets are nice as well, the Albert Cuypmarkt is worth a visit.
Renting a bike is much cheaper than travel by public transport and you can see a lot more, so thats's something to consider.
Hope i helped you out.
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