Out of the 4 days one day for Dan Haag.one day for Zanse Sans,one day for Brussels.As the trips can be done in the day time all 4 evenings can be kept for relaxing in Amsterdam.Which are the areas I should explore.
I see no one has responded to your question so I'll see if I can help out. I guess I'm curious why you aren't spending any days in Amsterdam - have you been there before and want to explore new cities?
For evenings in Amsterdam, I'd recommend taking a walk along the canals. The Van Gogh Museum is open until 10pm on Fridays. Depending on when during the year you're going, the Anne Frank House is open until 9pm or 10pm on Saturdays. There are evening canal boat cruises as well.
I'm glad you're planning to visit oft-overlooked Den Haag. I know it well, my husband is from there and I lived there for a couple of years. What do you intend to do there? The Mauritshuis reopens at the end of June, and Madurodam is better than ever. Strolling through the Binnenhof and around the shopping district is pleasant and there's a good herring stand right there - if you don't like herring, try the kibbeling.
I'm not sure you need an entire day for Zaanse Schans, but you could always do more in Amsterdam on that day.
To visit Brussels and come back all in one day, you'll have to start early, and you'll want to book fast train tickets on the Thalys service. They are very nice trains and you can nap and eat breakfast on the way. It takes two hours each way. Plenty to see in Brussels, and I'm sure there are a zillion threads in the Belgium sub-forum you can look in. I really like the MIM, the Museum of Musical Instruments.
The more famous sights in Amsterdam are mostly daytime ones - the Rijksmuseum, Van Gogh Museum, tours on canal boats, the Anne Frank House. The earlier you go, the fewer crowds, usually. The red-light district operates around the clock so you can stroll around there any time, although it's probably more striking at night.