Interesting Towns/Villages Near Amsterdam

One possibility would be Leiden - a short train ride from Amsterdam. Pretty university town (John Quincy Adams was an alum), plus you could see if you could find the Pilgrim Museum...fascinating place.

Haarlem is a interesting historical city, beautifully situated on the river Spaarne. Nice market square, two good museums (the Frans Hals Museum and the Teylers Museum) and the impressive windmill »De Adriaen« if you're interested in the working of this Dutch icon. Easy day trip from Amsterdam: 15 to 20 minutes on very frequent trains.
You will probably also like Hoorn, still showing its history as an important port and one of the founders of the Dutch East India Company. About everything in Hoorn is nice, and the Westfries Museum is well worth a visit. The half-hourly direct Intercity train brings you there in around 30 minutes. I like the second half of this trip, which goes through the classic Dutch landscape.
There are lots of other possible destinations within easy reach, among which of course my adopted city of Leiden, but you've got only one day...

I agree with all the suggestions you've gotten. I enjoyed Leiden, Haarlem, and Hoorn.

I went to Hoorn via the bus, which also stops in Edam, so I was able to visit both of those villages on the same day. I understand Edam becomes overrun with tourists on cheese market day (Wednesday in the summer), but when I was there, on a Monday in May, it was very quiet. I picked up a pamphlet from the TI that included a detailed walking tour, and I enjoyed it a lot.

Check out the bus link above, which has a number of other interesting excursions into the Dutch countryside.

I also recommend Leiden. You might also look in to the Zaanse Schans, it was about one hour by bus from Amsterdam Centraal Station

Zaanse Schans can also e reached in a very short trip by train and a 5 minute walk.

When in the spring? Late March through early May the bulb fields will be at their best and Keukenhof will be open.

... both of those villages
Don't call Hoorn and Edam »villages«. Although no longer of any legal significance, they are both proud possessors of city rights, dating back to around 1350.

This gives some information on Enkhuizen (as well as a lot of possible other destinations): www.holland.com/global/tourism/article/enkhuizen.htm. Enkhuizen is close to Hoorn: some 30 mins with 4 trains per hour.

If you don't already have it, get Rick Steves Netherlands. He has detailed descriptions for various daytrips from Amsterdam, along with goof-proof directions. You can see which ones interest you, and since there's no discount for advance purchase tickets on domestic trains and buses in the Netherlands, you can decide on the day where you want to go.

I enjoyed Leiden and Utrecht, and wasn't as taken with Delft or the Hague. I didn't like Haarlem but was last there in 1990, so who knows what I'd think now. However, while these are all smaller than Amsterdam, they are small cities, not rural villages. So, whether you should go to them depends on what you're looking for.

Depending on when you want to go in the spring, you may need to book reservations NOW. Tulip season (mid March to mid May) is a peak time in Amsterdam, and weekends year-round can also be very busy. So, for a weekend in April, it's not too soon to start looking for accommodations - and you may already be shut out of popular places.

Check www.localbus.nl Catch this bus behind the Central Station in Amsterdam. It's almost a hop-on-hop-off bus that goes through many nice towns. For 10 euro p/p it's a bargain

Thank you all very much for the feedback, looks like I'd have many great options.

Also consider Amersfoort, Alkmaar, and farther away, Delft. The very nearby early morning flower auction in Aalsmeer is of interest to some. I trust you understand that some of these ideas are not tiny wooden villages.

The beautiful thing is the Netherlands is easily traversed by train. Take a look at Haarlem and Utrecht. Utrecht, IMO, is like a small version of Amsterdam (800k to 300k population) and doesn't have the cheap tourism that plagues Amsterdam. And I think it's just as beautiful with regards to the architecture.

Some already mentioned places like Haarlem and Delft. Recently, a television programme featuring these and other historic cities in the Netherlands aired in the UK. So, if you would prefer some camera footage of what these places (and rail travel) are like, you can refer to episode 5 of BBC's Great Continental Railway Journeys: https://www.youtube.com/watch?v=bFjlPRmewhE .

Not too long ago we spent a fun day with the Waterland Bus Pass seeing nearby towns. We plan to do this again this May; is it now called the localbus that grrtgr references? It was a great value, we got tickets behind Centraal station for 10 euro pp back then.

You're getting lots of good suggestions for daytrips and I'll have one, too. But I'd like to recommend the excellent and often overlooked Dutch Resistance Museum in Amsterdam. Be sure to watch the film first.

As for out of town, no one has mentioned Keukenhof. If you are there at the right time, it's not to be missed. I can also recommend seeing the charming Bloemencorso. You could do both the same day, but be warned. That's the busiest day of the season for Keukenhof.

I'd strongly recommend the Mauritshuis museum in the Hague if you enjoy Dutch renaissance art. It's a fairly easy train ride from Amsterdam Centraal. The collection, for a small museum, is amazing, but it can be seen in half a day. The rest of the Hague was less interesting to us.
Delft is a charming small city, but it takes a couple of days to do it justice - lots of important Dutch historical sites, the Vermeer museum, and Delftware shops with demonstrations.

I agree with the recommendation of Haarlem - we try to stay there for a couple of days whenever we visit Europe.
Enjoy!

@ Denny ; Yes , that's the bus .Great bargain at 10 euro p/p and less for kids

Thanks, grrtgr, that's good to know.

I second the nomination of Keukenhof.......Keukenhof in the spring is stunning. Definitely worth a day trip!