If you don't want to rent a car, the Netherlands is easy by train. Trains are frequent, distances are short, most stations have luggage lockers (all the main stations do), and there's even a fairly affordable way to book a combined train & taxi ticket.

I've been to lots of places there without ever renting a car. Even rural places are often reachable by bus, but of course that won't work well if time is short. Still, Dordrecht, Den Haag, Delft, Leiden, etc., are all worth visiting and easily workable by train between Brussels and Amsterdam. There are easy day trips from Amsterdam, too, but honestly I think there's plenty in Amsterdam to occupy a few days (but then, I'm big on museums).