I plan on being in Bruges at the beginning of June.
From your experience, what would be 3 good day trips by train from Bruges. Small towns would be great. I’m not into nature walks.
Ypres for the history
a ride on the Coast Tram and hop on and off as the spirit moves you
Gent /Ghent is bigger than a small town but still most excellent
I know what you don't want - nature walks, and none of the above are that. I don't know what you do want, so hard to be specific.
I will second Nigel's recommendation for Ghent. In fact, I stayed in Ghent for three nights and took a day trip to Bruges, and loved Ghent so much. It is a very charming and interesting town, with lots of things to see and do.
Agree that Ghent is a good day trip from Bruges. A bike ride along the canal to Damme and have lunch in Damme (very small village). We went to Ostend for a seaside town day.
I know you ask for daytrips by train. Nevertheless here a few options for biking near Bruges in case it is off interest too.
Weather can be perfect early June for biking to Damme. With the open land wind can be a challenge or if you want to cover larger distances you can rent an e-bike. Worth doing is biking further along the canal to Sluis just across the border in the Netherlands. Both Oostkerke and Sint-Anna-ter-Muiden are worth a detour.
In Damme you can climb the bell tower, fantastic views from the rooftop with the skyline of Bruges at the horizon. You can do the same in Lissewege, a bit lesser attractive, nevertheless worth to consider. Not to miss is the huge medieval abbey barn of nearby Ter Doest.
The most attractive place along the Belgian coast is De Haan, known for it’s Belle Époque architecture and the place Albert Einstein stayed for a half year before moving to Princeton.
His house is still there, but in private hand. You can get there taking the coastal tram from the railway station in Ostend. In opposite direction you can take the tram to Raversijde / Raversyde, a well preserved part of the Atlantikwall, including an Enigma machine on display..
Lille is one and a half hour by train. An attractive French city with a Flemish twist. Known for it's Museum of Fine Arts and if of interest you can visit the birth place of Charles de Gaulle.
Brussels is one hour by train, Antwerp takes longer. If you like museums, both are certainly interesting.
Would highly recommend this WWI battlefield tour: https://www.visitbruges.org/. We took it in 2011 and it’s still one of the best tours we’ve done anywhere, mostly due to guide Nathan (who appears to still be leading them even now)! Being from the USA, we didn’t learn as much about the Great War in school, especially compared to WWII. This tour was so informative, and a few of the museums, especially the In Flanders Fields Museum in Ypres, were spectacular.