Bruges for a week?

While I think you could spend several days in Bruges, a whole week might be a bit much. Certainly Bruges itself is worth a couple ofdays. Day trips to Ghent, Antwerp, Brussels and maybe Sluis are easily done. If anyone has an interest in WW I, and renting a car is an option, then a day trip to Ypres and the Flanders Fields sites could fill another day

Is there enough to do in the city and daytrips by train for a week in June?

In the city? No, absolutely not. One day is more than enough, including an overnight stay for the romantics who want to admire the illuminated facades.
Perhaps I should mention two specific activities for June 2027.
- 'Feest in 't Park' June 26, 2027
- 1/4 triathlon June 19, 2027

BUT ... Belgium is a very small country and has one of Europe’s densest rail networks. With approximately 3,600 kilometers of rail lines, the Belgian network connects all major cities and many smaller towns.

This makes it very easy to take day trips.
Take a look at a map of our country and note the location of Bruges, which is certainly not centrally located. It’s therefore important to first decide which places you want to visit in Belgium and then choose where to stay.

Here is the railway network map, which gives you a clear overview of the major hubs
https://www.belgiantrain.be/en/travel-info/prepare-for-your-journey/leaflets/global-map-train-belgium

My then-12yoa son and I spent most of a week in Bruges. We did a day trip to the coast to visit the Atlantikwall Museum (highly recommended) and had lunch in DeHaan (also recommend). Didn't get to the aquarium further up the coast. I have said several times that I wish we had done it the other way around next time (stay on the coast and day trip to Bruges). It was probably the third week in September, so a little past the beach season, which meant no crowds, which probably helped.
My suggestion would be to look over a large area for interesting accommodation that suits your needs and budget. As another person mentioned, just about everywhere is connected by rail/bus/tram. I would set the map on AirBnB (my preferred booking site, might not be yours) to include Flanders west of Antwerp and see what comes up.

I have loved Bruges and definitely think it is worth several days! But totally agree with CJean! Easy to get to great places!

Don’t forget about the long coastline, it’s easy to get to the sea for a break from any hot weather

Is there enough to do in the city and daytrips by train for a week in
June?

Absolutely. We spent 4 nights in Bruges and could have spent more. We also did a day trip to Ghent, and you could easily do another trip or two. We didn't rent a car; trains were easy. That said, there's a lot to see in Bruges but whether those many attractions will appeal to your family depends on your family's interests and whether they're "slow" versus hit-and-run type of tourists. An interest in history also is helpful for this particular destination.

https://www.visitbruges.be/en

Like everyone else I think a week is too long, and being so far west does not make it ideal as a base, but there are still a few places you could go from Bruges that might pique your interest and fill your time:

*the Belgian coast (Knokke-Heist (casino, flashy restaurants) down to De Panne (Family beach), Raversyde for WWII history)
*Ypres (Ieper) for WWI history (plus points for this one)
*nearby Damme for a bike trip along long canals
*Sluis in the Netherlands (also small like Damme)
*Ghent for medieval architecture that rivals Bruges
*Brussels and /or Antwerp

That is quite a lot, but Damme and Sluis are only little. It is really not a good base for anywhere beyond this - anywhere in Wallonia or the Ardennes is off the menu unless you wanted a second base in Brussels for part of the trip.

Lavandula

Thanks for all the responses. We are definitely interested in history, especially WWI/WWII and castles/medieval. Ypres/Flanders Fields is something I didn't know about, but I think everyone would like. We are slower travelers than we used to be for sure, we spent 4 nights in Bourton-on-the-water this summer and could have spent more. My kids love finding a local pub to eat at each night, walking around the town, finding parks for picnics, grocery shopping to see new foods.

Ghent seems like it might be more centrally located for daytrips. It doesn't look like it gets get as "high" of ratings, but it seems to have more actual sites to see so might be another city I'll look into.

Maybe this will be helpful - https://michelledamiani.com/around-the-world/ignore-the-guidebooks-choose-ghent. "I want a bustling town with people meeting in the street outside cafes and then stopping for a beer together. I want to be jammed cheek-to-jowl in restaurants beside locals who probably consider this restaurant their neighborhood haunt. I want to be swept away by architecture, imagining what it would have been like to walk these streets a century ago, or two, or three, or ten."

What about this statement ...

Ghent gives you everything Bruges promises—canals, medieval architecture, chocolate, beer—plus everything Bruges lacks: a real city with real residents, excellent restaurants that aren't tourist traps, and an energy that comes from 44,000 students rather than 44,000 daily visitors.
It's the Belgium that Belgians love. Go before everyone else figures it out.

Source: https://cityvoyagerhub.com/en/hidden-gems/ghent-belgium-most-underrated-medieval-city/

Perhaps google 'Ghent vs Bruges' to get some inspiration.