Amsterdam has the best train system for day trips. I recommend staying in the central area of Amsterdam for the ease of taking trains. The Netherlands is a small country with trains and buses going everywhere. They are on time, fast and leave frequently. Some are so close that it does not have to be an entire day.
Haarlem is about 15 minutes away from Amsterdam and trains leave about every 15 minutes from Amsterdam. Make sure you get off at Haarlem Central. It is a beautiful train station and is worth a look before you walk into town. Haarlem is a nice town to walk around in. The big sights are Grote Markt which is a big square that contains the Church of St. Bavo. which is a beautiful church worth a visit and the town hall. I would print off a Haarlem walking tour and spend some time walking around the city. The one site that I would recommend is seeing the Corrie Ten Boon. Corrie Ten Boon’s story was told in the book the hiding place. The door is not around the corner and not at the jewerly store. Check the open hours to make sure that you are there when they do a tour. I would also check the door to double check the hours, as it is not always what it says on the website. The only way to see it is with a tour. This is a wonderful tour done by volunteers.
Delft is one of my favorite towns in The Netherlands. Like most places, you can get there directly from Amsterdam Central. It is a small compact central area and you really can see everything in a day. I recommend getting a historic walking map. It is not free but you can get it either from the tourist shop or on the cities website. I took the walk and it really is worth the couple of euros. Some not miss stops is the Old and New Church. The New church sits at the top of the Market Square and really is not new. It was built in the 14th and 15th century and has the tombs of many of the royal family. The Old church was built around 1250 and has the distinction of leaning two meters off center. Vermeer is buried there along and I have been told that since the last time I visited, they have put a new larger memorial stone as it was pretty easy to miss before. Many people go to Delft for the famous blue porcelain Royal Delft. Just outside of the center you can visit Royal Delft experience where there are tours and a store. Be careful if you want to buy Royal Delft and buy it outside of the factory store that you are getting the actual real stuff and not just some junk from china. But the big thing in Delft is just to wonder around this city.
Will thinking of Holland and Amsterdam most people think of Windmills. While there really is not any good windmills to see in Amsterdam, it is a short trip out of the city to see them. Zaanse Schans is a 15 minute train ride out of Amsterdam Central and is an open air museum. There are eight preserved windmills, some that you can tour for a small fee. I went off season so there were not many tourist. While it is clearly very touristy, it is a great way to spend the afternoon and get out of Amsterdam. There is a bus that gets you right there that takes forty minutes, but I prefer the train which takes you to the Koog-Zaandijk stop from Central Amsterdam. There are plenty of signs that will lead you to the wind mills which are about a 15 minute walk from the train station. I like that walk because there is a great view while you walk across the bridge to get there as well as a great little restaurant across from the windmills. You also walk by a Nestle Chocolate factory which smells amazing. The entire area around the windmills is a fantastic walk and is the perfect day trip.
There are many more great day trips, but these are my favorite. Leave your suggestions in the comments.