We will be in Gouda for a few days in early June and would like to do some day trips by train to cities that are close by - Rotterdam, Dan Hague, Delft, Leiden are all on the list. Since we only have a couple of days, I'm wondering which ones we could practically combine in one day. Open to other suggestions as well.
It depends on what you want to do in each of the cities. Den Haag and Rotterdam both have museums of some size (though Rotterdam's Boymans van Beuningen is currently closed). If you mainly just intend to walk around outdoors, that will reduce the time you'll want to spend in those cities. And, though Rotterdam is a large city, its architecture is mostly modern.
Dutch domestic trains are tap-to-pay, so you don't necessarily have to plan your train trips ahead of time. You can head to Leiden, for example, and decide after you've been there for a few hours whether you want to visit a second city that day or spend all your time in Leiden. There is a possibility of a discount on some rail tickets if you buy a departure-specific ticket in advance, but I think most folks don't do that. Such offers will pop up, when available, if you check a schedule on the website ns.nl.
Edited to add: My sightseeing interests are atypical, so this probably will not help you, but: I spent about a month in the Netherlands earlier this year. I spent multiple nights in each of Rotterdam, Den Haag and Leiden. I opted to make Delft a day trip, though I suspected I'd be tight on time there. I was right in all cases (loving art museums and Art Nouveau architecture as I do); there was less for me to see in Delft, but I would definitely have enjoyed an extra half day or full day there.
Travelling between these cities is easy and fast. Gouda to Rotterdam or Gouda to Den Haag / The Hague takes without changing trains around twenty minutes or a bit more. Train or even tram between Rotterdam and The Hague around a half hour with Delft halfway in between. Due to maintenance work it will take longer according the time table, but only this weekend. So no worry for coming June.
For planning you can use the planner of our national carrier NS: https://www.ns.nl/en
As soon as you know what to see and visit as acraven says you can be very flexible moving around. For other modes of public transport you can use this planner: https://9292.nl/en/
the other end of the short train line between Gouda and those cities to the west, Den Haag and Leiden and Rotterdam and Delft, is Utrecht where the trains come from, just a short ride the opposite direction.
A lovely place is Utrecht, with the canals down below, and some special and unique museums.