We are taking a cruise from Ireland to Iceland in mid-May. After the cruise we are extending our trip nine days, flying from Dublin to Brussels. I anticipate that exploring Brussels, Bruges, Ghent and Antwerp will take about six days (?). That gives us a few more days to explore other parts of Belgium or nearby countries. What are other nearby destinations worth visiting? After spending time in the cities, something quieter with access to outdoor activities would be great. Luxembourg? The Ardennes? Somewhere on the North Sea? Nearby France or Germany? We won't have a car, so easy access by train/public transportation is necessary. Thanks!!
Depending on what you are interested in, you could certainly spend more than six days (five nights or six nights?) in Brussels, Bruges, Ghent, and Antwerp. I loved Bruges and Ghent themselves. Some people take World War I battlefield tours (I didn't). I didn't care for Antwerp too much, but there are more museums there now that would interest me than when I visited.
I also enjoyed a day trip to the town of Leuven near Brussels.
For example, you could do two nights in Ghent, two nights in Bruges, two in Antwerp, and one in Brussels or Leuven.
Even if you spend only six days in Belgium, you don't exactly have a lot of extra time to see much of another country. I think I'd base your final few nights based on where you can fly out of - if you aren't going to spend the whole time in Belgium, then look into flying home from Amsterdam or Paris (most likely the best connections) or from say Luxembourg City. I'd pick one of those and just spend the last 2-3 nights there. If you've already booked a flight home out of Brussels, then I'd probably head for Luxembourg City or Amsterdam for a few nights first, then end the trip in Belgium, probably in Brussels, Leuven, or Antwerp (all direct train connections to Brussels main airport).
Parts of Belgium are noted for outdoor activities, but I haven't visited those areas. It may not be that warm in May, but the Belgian coast combines both some World War II sites and wide sand beaches. Ostend is quite a "party town" in hot summer season, but is quiet off season. It's associated with the surrealist painter James Ensor.
I assume you mean hiking and scrambling when you say outdoors, but Antwerp is a very large city that requires a lot of walking to see fully. For example, on weekends, the large Rivierenhof park is busy with families, concerts, a small art pavillion, the old Silver Museum castle (don't know if it's still open). Antwerp has a major landscaped sculpture park that takes a while to see, and the walk from the nearest bus stop is a hike as well. (Sorry, that counts as Outdoors to me!) I even took a bus to the end of the line and walked to the Antwerp Airport, which is a almost defunct today.
Antwerp has a large, lovely 19th Century townhouse district (exteriors only) which is 2 hours of strolling, called Cogels Osy Lei. It also has pedestrian walkway under the river. I took the subway tram back, but you could also walk.
If you don't elsewhere for hiking, other Walloon cities worth visiting (by train) include Mechelen, Leuven, Lier, and Turnhout. They each have some special museums and sites. Here are some past discussions:
You can see the marvelous cities of Gent, Bruges and Antwerp in 4 days (skip Brussels).
That leaves 5 for Holland.