First answer for me would be to fly, however your optional stops make train more reasonable. If you want to stop in Brussels, I’d take one of the direct London-Brussels Eurostar trains — fares as low as £35 and only 2 hours (+/- 1 hour time difference ) so faster than flying. Brussels to Basel, I’d normally look for a cheap flight. While there are train options as fast as 5 hours, the fastest option requires backtracking to Paris, RER from Paris Nord to Lyon Banlieue and then walking to Gare de Lyon— not my idea of a fun day. However, there’s an option with a single connection in Frankfurt which takes over 6 hours, but less than 3 hours Brussels to Frankfurt and less than 3 hours Frankfurt to Basel. Perhaps train one way with stops in Brussels and Frankfurt and fly back??

Driving all or part may be expensive since there are several countries involved which increases rental car prices — particularly if you pick-up in one country and drop off in another. Neither Brussels nor Frankfurt is my idea of a pleasant drive, but you could have an enjoyable drive once you’re outside the cities and if budget will cover it. It would certainly be an interesting way to explore Switzerland, although I ‘d hesitate to drive if traveling solo. IMO, driving in a foreign language is a 2 person job. 1 to drive and 1 to navigate and “spot.”

Check Easyjet.com. Depending when you go, I see some one-way flights as low as $49. Mind the fees. If you have a lot of baggage, then BA or Swiss might be cheaper overall. http://www.skyscanne…

Thank you for the feedback, I have a 7 year old, that would be accompanying me everywhere. I am still confused. Seems like flying is the best option.
Sometime in 1996-97, I was in Belgium for about 6 weeks and drove every nook and corner including driving over to Paris and back. I guess much has changed between now and then.
Recent times, I normally take the train from London to the client in Brussels and back the same day.

Let me post messages on transportation to see what folks are doing?