I stayed at the campsite at Grimbergen last August: http://camping-grimbergen.webs.com/
We left our bikes locked up to a tree, and used public transport to get into Brussels to see the sites.
There is a bus stop about 200m from the campsite where you can get a #232 bus to De Wand (takes about 20 minutes). At De Wand you can purchase a day ticket for Brussels and then get a #7 tram to Heysel (to visit the Atomium). You can then get the Metro at Heysel (line #6) as far as Beekant (8 stops). At Beekant change to line #1 (adjacent platform) as far as De Brouckere (4 stops). The old central square of Brussels is about 400m from De Brouckere.
Traffic in Brussels is pretty bad, especially during rush hour. Our bus back to Grimbergen was 30 minutes late.