How long do you have in each country and where exactly are you planning on going?
For the Netherlands, I can recommend the following:
- do NOT rent a car. We have excellent public transport and you pay through the nose for parking anywhere in a city centre (we do this on purpose, as our city centres were not built to accommodate a lot of cars). The trains even give you a discount if you travel in a group. Get a temporary OV-Chipcard (it's a card you put money on to ride) for everybody if you want to use public transport. Unfortunately, the system isn't always clear for non-Dutch speakers. Ask for help if you don't understand, pretty much everybody here speaks English. If you have more than 2 or 3 days here, I recommend seeing more than 1 place and going there by public transport.
- I am a proud Amsterdammer, so i definitely recommend going there. However, this is also the obvious choice - will give you some other tips later on. In Amsterdam, if you're remotely into art at all, visit the Rijksmuseum and the Van Gogh museum. They are not the cheapest thing to do around, but they are SO worth it! The best free entertainment is just walking around town - it's the best way to get to know the place, really. I love just ambling along the canals and soaking up the atmosphere. Just watch out for bikes, we Dutchies cycle everywhere, and Amsterdammers (including me) ride like maniacs and expect lowly pedestrians such as yourselves to make way when you're not on the sidewalk. Also, we have some pretty nice parks to walk and sit in. Buy picnic supplies at a supermarket and have a cheap lunch there when the weather is nice. For a nice, free view and an affordable cup of coffee, visit the public library near Central Station, there's a café with a rooftop terrace. Some nice lively places to visit and people watch at 0 cost: the weekly biological market at Noordermarkt on Saturday, the Albert Cuyp market, the flea market at Waterlooplein (both every day except Sunday). Another relatively affordable activity is renting a bike for an afternoon and just cycling around town, or going for a longer cycle in the beautiful countryside just outside Amsterdam (highly recommended is cycling along the IJsselmeerdike to Durgerdam, and if you're really into cycling, all the way to Marken). Another 0 cost nice place you shouldn't miss is Begijnhof and it's 2 churches. The entrance is in the middle of the main shopping disctrict, and it's like stepping into another world. Take the free ferry to NDSM werf behind Central Station when the weather is nice. The view on the water is cool, and NDSM werf is a former wharf which is being regenerated. There's still some rough edges to it (regeneration started with squatting artists), and it has several really nice places to eat and drink, with views on the water. If you're into classical music at all and here on a Wednesday, try getting into the free lunchtime performance in the world-famous Concertgebouw. It starts at 1230, but you should arrive early!
- Amsterdam still has a shortage of hotel rooms, which drives up prices. Book in advance, shop around on booking.com for good deals, and definitely also consider AirBNB (airbnb.com). Hotels that are a bit further away from the city centre are loads cheaper, this could be well worth it even with added public transportation costs. There's also this:
http://hotelschool.nl/en/hotels-restaurants/skotel-amsterdam#!rooms, it's the training hotel for a prestigious school for future hotel employees. Also check youth hostels, they often have reasonably priced family rooms available.
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If at all possible, do NOT just stick to Amsterdam. Haarlem is only a 15 minute train ride away, and is pretty much as beautiful, but smaller and a lot less hectic and touristy. Here also take the time to walk around the city centre, it's gorgeous. And step inside the St Bavo church (they charge admission these days but not very much). Haarlem has 2 very worthwile museums: the Frans Hals museum (gorgeous paintings by Dutch masters) and the Teylers museum (science and technology). Teylers really is worth it, it's the oldest museum we have and contains lots of weird inventions from when we were actually at the forefront of science a few centuries ago. Haarlem has lots of hofjes (like Begijnhof), check them out, they're usually free and very pretty.
- From Haarlem, there's trains going on for another 15 mins to Zandvoort, i.e. the beach. The town itself is really quite ugly, but the sand dunes and the beach are well worth a visit for an afternoon walk (just hike along the beach and back through the dunes or vice versa) and for watching the sunset.
- Utrecht is also a nice place to visit and walk around, with a smaller and less hectic city centre than Amsterdam. It's about 20 minutes by train from Amsterdam Central. There's beer cellars along the canals which now house restaurants and pubs, so you can have a drink at water level - do that! I recommend Museum van Speelklok tot Pierement
https://www.museumspeelklok.nl/, dedicated to automated musical instruments, and the Spoorwegmuseum (reached by a special train from utrecht central)
http://www.spoorwegmuseum.nl/, dedicated to the railways - these are especially nice if you have children.
- The Hague is the only Dutch city which actually has beachfront access, so you can combine a city trip with nature / beachcombing. It's about 40 minutes by train from Amsterdam Central. Here, visit Mauritshuis (one of the best museums in the Netherlands), poke around the houses of Parliament at Binnenhof for free (who knows, you may run into a prominent Dutch politician, they're definitely a lot less heavily guarded than yours). ProDemos has affordable guided tours, on which you can visit the inside of these buildings. See here:
http://english.prodemos.nl/English/Visitor-Centre/Guided-tours. Take a tram to Scheveningen or Kijkduin and walk on the beach for free. And here also: walking or biking around is the best way to see the city centre.
- Halfway between Amsterdam and The Hague is Leiden. It has a very large university in a small, historic town, so there's a decidedly studenty feel to the place. Lovely city centre to just walk around in, lots of greenery where the old city walls and fortifications used to be, and lots of affordable places to eat and drink (because duh, students). The very old university has spawned some pretty good museums: I recomment the Museum of Antiquities (Rijksmuseum voor Oudheden - hosts classical Greek, Roman and Egyptian art), the Museum of Ethnology (Rijksmuseum voor Volkenkunde - hosts art from all over the world, mostly from our former colonial empire) or Naturalis (the museum of natural history).
- Rotterdam is the 'other' large city in the Netherlands. It was heavily bombed in WWII, so the city centre is mostly concrete - it's the only Dutch city with an actual skyline and lots of modern architecture, some of it quite experimental. However, I think it still merits a visit. It's about 50 minutes by train from Amsterdam. The recommended museum here is Boijmans van Beuningen - art, but from more modern days than the other spots i recommended. Definitely try to walk or cycle across the vey impressive Erasmusbridge across the river Maas, which runs through the middle of town. Have a drink at the atmospheric and artfully renovated Hotel New York - where immigrants used to leave for America. The neighbourhood of Delfshaven is reachable by metro from Rotterdam Central, and has survived the war so it's nice for strolling around.
- On your way to Rotterdam, you'll pass through Delft. This is also well worth a stop. It has a very beautiful historic city centre, great for just walking around in or sitting somewhere with a coffee.