Four full days in Netherlands. Base in Amsterdam or other city?

Amsterdam is very busy. If you don’t like crowds, Leiden and Utrecht are two really nice sized cities that have lots to see and do, a decent buzz but not as crowded as Amsterdam. Utrecht in particular has really good rail links to other small towns (I stayed there and enjoyed a mini-trip to Gouda). It is also extremely interesting for architecture and museums.

Haarlem is pretty but smaller than either Leiden or Utrecht and I felt there was a lot less to see and do.

Well, I happen to love Amsterdam and hate to shortchange it, but if you're better off in a smaller town, you can't go wrong with the two that Golden Girl recommended. I have not been to Utrecht (yet) but took a day trip to Leiden and loved it. And when I go back, I would definitely consider staying there for a longer period of time. It's only a quick 30 minute train ride from Amsterdam and the other small towns around are easily accessible from there by train.

It's also a beautiful university town and the home of Leiden University, which is one of the oldest universities in the country. Leiden has a wonderful atmosphere, too, with charming cobblestone streets and 17th century gabled houses. It has many historic buildings but does not have the "touristy" feel of many other places. It's a much more livable feel. The city has many picturesque canals and waterways, which are lovely to walk along and there are boat tours you can take. And there are lots of parks, gardens, and green
spaces in Leiden.

I did not care for Haarlem that much as it was very crowded with tourists the day I was there (in May), although I did like the Corrie Ten Boom museum. I'm glad I went but I would not really care to stay there.

Leiden is a bit handier if you are looking to include Rotterdam/Delft/Den Haag in the plans in addition to Amsterdam. It is only a short ride (15-20 minutes) on frequent trains from/to the airport, about 40 into Amsterdam, and about the same to Rotterdam, with Delft and Den Haag being less.

I would recommend Amsterdam for a short stay like yours. I don't know if there is a better city for walking, architecture and vibe. If it fits your needs, check out sweets.com (accommodation in former bridge houses). Otherwise, this site has lots of good restaurant and hotel recommendations.
It can certainly get crowded, depending on the time of year you visit. Whenever you go, you will need reservations for some of the museums (Anne Frank, Van Gogh and Rijks, maybe others). There are lots more, including the Eye Film Museum, Resistance, NEMO Science. While there is certainly a lively club scene, it's easily avoided (to the point where I couldn't tell you where to find it).
I have done two after-dark canal tours with Those Damn Boat Guys and found both very enjoyable. I don't think they are the most thorough as far as taking you past historic places, but I like the small boats and personal commentary. And if your captain suggests getting dropped off at the marina instead of returning to the pick-up point, say yes! It's not far away, and there is a very fine pub around the corner in this quiet residential area. Others on the Forum like Captain Jack's. These smaller tours require reservations. There are big-boat tours that probably don't.

You can’t see Amsterdam in just four days. Since convenient day trips by train are very easy, you are not restricted to Amsterdam anyway. Previous replies are accurate and helpful. It depends on your desires.

Book Anne Frank House well in advance or you’ll not get in.

Interested in history, architecture, museums, walking, general vibe

Amsterdam has all this in amounts far greater than 4 days can cover and to a greater extent than any other Dutch city. And Amsterdam has a ton of nice places to eat and stay.

My usual grouping of Anne Frank House, Dutch Resistance museum, and Corrie Ten Boom house are spread out enough to give you a few different areas to see (two in Amsterdam, one in Haarlem), and really only the AFH is crowded (on the outside area). Haarlem was a lovely day trip, but compared to all the offerings in Amsterdam, it wouldn't be my suggestion for a first (and shortish) visit to the Netherlands.

You can definitely avoid "massive" crowds by not spending much time in the more "core" touristy areas (say from Dam Square down through the Red Light District and ending by Centraal station).

But I wouldn't avoid those areas altogether - just choose maybe less "peak" hours to wander through? Amsterdam is a living city, so there is always activity - locals and tourists - but you can also pop out into parks and even the "countryside" with relative ease.

If you are going for a very RELAXING break, though, Leiden for sure was a notch down in activity, but also full of options for exploring, as was Delft. Haarlem, Delft, & Leiden would all be relatively near Den Hague, Rotterdam, and Amsterdam, so you could stay & relax in those lower key spots and then simply make a day trip or two out to the bigger cities if you wanted a bit more action.

Honestly, with so much to see and do, all the Dutch cities will work as a home base and have lots of options for fun filled days.

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You can’t see Amsterdam in just four days. Since convenient day trips by train are very easy, you are not restricted to Amsterdam anyway. Previous replies are accurate and helpful. It depends on your desires. Book Anne Frank House well in advance or you’ll not get in.

Thanks. I don't intend to see all of Amsterdam in four days, but four days -- actually 4.8 days -- is what I have. The idea to stay in another location was not because I feel I'll have exhausted Amsterdam, but just to save money.

Since I just decided to do this trip, I'm aware Anne Frank house tickets are no longer available. My understanding is that the museum issues some same-day tickets. If that's true, I'll try to get one of those, but if not, that's OK.

... Amsterdam, but just to save money.

In that case, I would definitely "shop around" to those smaller cities. You don't lose out at all by staying in the places like Leiden, Haarlem, or Delft. They are lovely.

I personally don't think that you can go wrong opting to stay there because 1) they have plenty of nice things to see and do in a 4 day window, and 2) they are still insanely close (by American standards) to the bigger cities.

Thanks. I don't intend to see all of Amsterdam in four days, but four days -- actually 4.8 days -- is what I have. The idea to stay in another location was not because I feel I'll have exhausted Amsterdam, but just to save money.

Thanks for your prompt and courteous reply. I've daytripped to Leiden and Utrecht each twice, and they are superb visits. Neither of those places can be "seen" in one day. I've also day-tripped from Amsterdam to Haarlem, Delft, Amersfoort, and Alkmaar, each of which can be seen in a day.

As a native of a large city (NYC), I want to remind you that for your short visit, your time is Money. I imagine you're younger and more energetic than I am, but commuting to Amsterdam is a big chunk of time out of your day, and you only have a few of them. Leiden and Utrecht both have wonderful museums, but there are a few world-class museums in Amsterdam that you really need to see. As you may know, a comprehensive national museum is quite hard to survey in just one day. A lot of things close at 5PM ... ...

American public transit isn't as good as in the EU, but they have a still-useful saying on Trip Advisor/NYC: "To visit NYC, stay in NYC." Just one opinion.

... commuting to Amsterdam is a big chunk of time out of your day...

Not really. As noted above, Leiden is only 30 minutes away and if you stay near the train station, which is a nice area, you could easily get to and from Amsterdam and other places in no time. And depending on where you stay in Amsterdam, especially if you're on a budget, it could easily take you almost as long to get to the main sites.

moss, by the way, you might be interested in this mini trip report posted by a long-time member here who stayed in Leiden with her husband for four full days: https://community.ricksteves.com/travel-forum/trip-reports/one-more-mini-trip-report-four-days-in-leiden-and-one-night-at-a-schiphol-hotel

My understanding is that the museum issues some same-day tickets. If
that's true, I'll try to get one of those, but if not, that's OK.

You didn't say what your travel dates might be, but I'd check the Anne Frank house for tickets on Tuesday just before 10 a.m. Amsterdam time both one and two weeks ahead of your dates. Occasionally they release a batch of tickets then. Be sure to use the official website and not a third party. You might be put in a "waiting room" for tickets, just be patient - https://www.annefrank.org/en/museum/tickets/