'S-Hertogenbosch for Bosch 500 exhibit

I am afreed ´s-Hertogenbosch is not the most central location for daytrips, but you can consider:
Antwerp in Belgium, 2 hours each way by train.
Kröller Müller (Van Gogh) Museum near Otterlo needs about the same time, several changes bus and train.
Kinderdijk Windmills combined with a visit to Dordrecht. https://www.kinderdijk.com/travel-info/transportation
Disney style themepark De Efteling. Not the best period now for outdoor activity, heave no idea which attractions are not in use this time of the year. https://www.efteling.com/en/park
Utrecht, ½ hour by train.

Likely you will need all the three days for Amsterdam, so using your four days as much as possible for the daytrips.

You'll love Kinderdijk, but it involves close to 2 hrs travelling. Dordrecht is a better option. Lovely city, undeservedly much overlooked. Only 1 hr from Den Bosch by half-hourly train.
Utrecht is another good suggestion. You'll love the lively area around the Oudegracht.
Closer by you've got Heusden, an restored historical fortified town. The half-hourly bus takes some 30 mins.
All connections - train and bus - can be found at the public transport planner http://9292.nl/en#.
Enjoy!

Thank you both for your reply. I am going to research Utrecht, Dordrecht, and Heusden and share with my husband. I appreciate your suggestions!

We just went to Den Bosch for the exhibit last weekend and it was really nice. It's a little random, but we were on the train from Amsterdam to Den Bosch and saw a cute looking village out the window on our way there. On the way home, we decided to stop in the town. It's called Culemborg. It's about 25-30 by train from Den Bosch. There isn't much to do but it's quaint, has a working windmill, a couple churches and a pretty market square with a good Belgian beer cafe. It's also close to Utrecht so you could combine it with Utrecht for a day trip if you wanted.

The Bosch exhibit is really well done but crowded. Trying to get up close to the paintings took quite a bit of time. It's also fun to see the town full of Bosch characters :).

Culemborg, although a town (don't call it a village!) with an impressive history and nicely situated on the river, is a good stop, but too tiny to warrant a day trip.
But it reminded me of another nearby river town, Zaltbommel, which can also boast of a city charter going back to the early 14th century. It's only 10 minutes on the half-hourly train from Den Bosch.

I agree with Jennifer and Ton about the quant places mentioned who are really nice. For some variation thinking about a castle or a palace will be nice too like Paleis het Loo near Apeldoorn, however needs some 2 hours to get there. Closer to ´s Hertogenbosch is medieval castle Kasteel Ammersoyen, about a half hour with the bus, but in March only open for visits on Wednesdays and Sundays.

https://www.glk.nl/landschap-kastelen/locatie?locatie=15 (limited English info)
https://www.paleishetloo.nl/en/#2016-03-01

Thank you all for your replies. I think we will do Heusden or Culemburg and Utricht. We are looking forward to this trip and especially the Bosch exhibition!
Lisa

If you like to stay in the Southern Dutch atmosphere you could consider a day trip to Maastricht. Wonderful town near the German/Belgium border.
It is often overlooked by tourists, but known by the Dutch for its beauty and Burgundian lifestyle.
It is 1:30 minutes by direct train connection from Den Bosch.