Yes definetely! I can recommend the 'GR' routes (Grandes randonnées), which are indicated with a small red and white flag. These hiking trails are well kept and usually hit the nicest places.
The hiking trails that are on and around the Hautes Fagnes are magnificent (I believe part of the GR 5, valley of the Hogne), but a bit hard to reach by train. You could try via Eupen or Verviers, but you will still need a bus or try hitchhiking. Maybe you should try to spend two days.
If you really want to do some walking for one day, I would just take an early train to Verviers and than a TEC bus in the directiion of Robertville/Rocherath (line 390, not many connections!). Make sure to get out at the Signal de Botrange, the highest point in Belgium and heart of the Haute Fagnes (a big swampy moor, really nice)
A less well known part of the GR network runs from Vielsalm to Spa, and is probably easier to reach by train and almost as pretty.
The link underneath offers an overview of all the GR routes in Belgium. site in Dutch though) I would just take a look at the overview and buy the appropriate 1:25000 scale walking maps, and you should be fine. The trails are usually very well indicated.