You can go to the Flemish tourist office in the Grasmarkt and buy a map with the cycle routes from Brussels to Antwerp. It's not that far between the two cities so you could even try to cycle it in one day. Beware though : you will be cycling in the most densily populated area of Flanders and will see more industry/cities than nature. If you want to enjoy the feeling of cycling on car free roads, you should take the train from Brussels to Sint-Truiden or Hasselt. In the tourist office there you can buy a map of the local cycle network. This part of Belgium was elected as the best cycle province of Flanders. You can visit Tongeren (famous Sunday antiques market), Borgloon (pitoresque city in the fruit regio), Hasselt & Genk (both very trendy with hotels with extremely good price/quality ratio)... From Hasselt you can take the train to Antwerp. If you are really a good cylist you can even cycle from Sint-Truiden to Lommel and take the train to Antwerp from Lommel. Enjoy your stay!

With the high speed trains, you could easily do a weekend in either London, Paris or Amsterdam. They are all within three hours travel time from Brussels. If you are in Europe now already, you are probably a bit too early for the lush green fields. Officially it is not spring yet. But the best place to go will probably be Borgloon in the north east of Belgium. You can take the train from Brussels to Sint-Truiden and then a public bus from there to the little town of Borgloon. There are a lot of hiking routes in the area, so the tourist office should be able to help you out. The area is hilly, but because most of it is comprised of farm land and orchards, you have a lot of unobstructed views of the landscape. If you prefer hiking in the forrest, the there is also the Ardennes in the south of the country, also easily reachable by train. And with a weekend pass, you can travel anywhere within Belgium to and and from, for the price of a normal single ticket. Another great option is Keukenhof in the Netherlands. It will open shortly and you can enjoy fields and fields of brightly colored flowers. It recently snowed one or two weeks ago in Brussels, but it is very rare this late in the year and is unlikely to happen again. You would probably have to travel to the ski resorts in the alps, either in France, Switserland or Austria. With just a weekend to spare, there is no fast way of getting there other than flying or perhaps taking a night train.