We've got up to four days in Amsterdam at the end of our trip. I am looking for a few good day trips out of Amsterdam so I might see more of the Netherlands. We would zip over in the morning and return by evening. Our main requirement is that the place we visit be reachable by train or bus, preferably under 1.5 hours of travel each way. There is no point in spending most of the day riding about the countryside. We prefer not to have to rent, drive and park a car.
Personally I am always very charmed by Enkhuizen, 1 hr from Amsterdam with a half-hourly direct train service. A small-scale historical harbour city, one of the founders of the Dutch East India Company, which can keep you busy for the best part of a day. The Zuiderzee Museum is an open-air museum, recreating the times when the area still had an open connection to the North Sea.
More information on the website of the regional tourist office.
Alkmaar is nice. Meets your crteria for train travel and is an easy walk from the station to the city center. If you go on a Friday, you'll see the recreated cheese market, Saturday for the outdoor market.
The pretty windmill village of Zaanse Schans is a short train ride away. Best to get there early or late - it gets crowded with day trippers and tour groups at midday.
We particularly enjoyed the town of Leiden. The Pilgrim Museum there was an unexpected find, and the town itself is just a pleasant place for an extended stroll.
Another possibility would be to rent bikes and explore the beautiful (and flat) poulder country in the Waterland area just north of the city. There's a free pedestrian/bike ferry that takes you across the river, after which you have miles of pretty, off-the-beaten-path choices for a meandering ride thru the countryside. The old eel fishing village of Marken is one particularly nice route, and Marken itself is a great place to explore and maybe grab lunch before heading back.
Leiden, Delft/Den Haag, Haarlem, Utrecht, Amersfoort, Alsmeer (flower auction A.M. only). You did not give the month of the year, so we don't know if it's tulip-time. Alkmaar and Gouda are perhaps a bit touristy but also nice. On this list, Leiden and Utrecht can't be seen fully in one day, but are worth a visit. In Den Haag, some visitors will want to prioritize the two big museums, rather than street-strolling.
Do you have Rick's Amsterdam and the Netherlands book? In it, he describes all kinds of day trips, from cities to rural areas, complete with goof-proof transit directions.
@Harold - I had the RS guidebook to the Netherlands. But, I followed his advice and tore it up into smaller sections which I left for other travelers as I left each area. :-( What is that saying "No good deed goes unpunished"? :-)
Have you thought about the www.localbus.nl tour? Goes from Amsterdam Central Station to Volendam, Marken and many more quaint towns and villages .. 10 euro for the whole day so you can wander around a town and when one of their busses comes by you just board it , repeat as many times as you like .
Is there a reason you want to stay in A'dam to day trip. It sounds like you've been there before.
Barnstormer, I'll second Ton's recc. of the Zuiderzee museum in Enkhuizen. It was easy to get to, and once there we used our museumkaarts to get a ticket to ride a shuttle boat from town out to the museum area. We spent most of the day there, breaking for lunch in their lovely cafeteria, and late afternoon walked back toward town so we could stop at the indoor museum part and browse. It was quite interesting with some large boats, period costumes, housewares, etc. The painted step stools were my favorite thing there.
Another plan would be to go to Leiden and visit the Pilgrim museum. Seems to me the entry was 5 euro each and our tour lasted almost two hours. It is open limited days so you would want to research which day to go. Of course there is quite a bit more to experience in Leiden but that was my favorite thing.
A third good option is Delft. The small city is wonderfully walkable and the Prinsenhof museum was fabulous.