My family is planning a trip to Europe in the spring. We are wondering what is the best way to get from Heidelberg to Lucerne, while spending a couple days in the black forest. What should we see? Do? Or experience? Baden-Baden's spa is out. We are renting a car, so transportation is not an issue.
With a car, just drive south along A5. The Black Forest will be to your left, the upper Rhine to your right. My advice would be to concentrate on the southern Black Forest, as the mountains are the most impressive here. Consider Freiburg or Titisee-Neustadt as a base. Alternatively, you could drive along A81 south from Stuttgart, which runs through the Swabian plateau along the east side of the Black Forest. The mountain scenery isn't as impressive here, but there's a few advantages. One, it's a more direct route to Luzern, and you're not missing much in the way of scenery from Basel to Luzern anyway. Two, you can make a short detour to see Burg Hohenzollern outside of Hechingen, and perhaps stop in Tübbingen along the way. Three, this route allows you to enter Switzerland via the Bodensee, which is one of the most stunning corners of Europe for scenery (on a clear day, anyway).
Just to add a little to Tom's response, if you take the A5 route toward Basel, a really pretty town to visit is Oberkirch, about 15" east of Offenburg. Also, a short drive west from Freiburg is Colmar, France, one of the prettiest towns in Alsace. If you want to see one of the world's greatest flower parks, then stop to see Mainau Island, which is just outside of Konstanz. Best route? I'd suggest the A5 as far as Freiburg, then B31/B33 via Titisee-Neustadt to Konstanz.