Hi,
If you want to be exploring battle sites from WW1, other than my suggestion above on Liege (Lüttich) and Mons, a few places have been mentioned above, such as Tournai and especially Dinant. In 1914 that town was in the path of the German advance according to the war plan, the advance of the Saxon Army, (the German 3rd Army) who were sniped at, shot at by civilians in that town, which the German command saw was against the rules. As a result numerous reprisals were taken, hostages (innocent and guilty) were shot, etc., etc. ...just bad, period.
In May 1940 again due to its strategic location, Dinant was right at the beginning of the action which would result in the events at Dunkirk.
If you do get a rental car and explore southern Belgium. I second the suggestion on going across the French border to see Sedan, the site of one of most complete encirclement battles in modern European history. Traces of that event are still there, ie, remnants of the ramparts.
Bottom line.....go to southern Belgium. I've yet to see most of it, only have been to Charleroi, itself historical due to its location on the Sambre.