"We will be spending three nights in Freiburg in June..."
The charm of the Black Forest resides in its smaller towns and villages, where townfolk lead a somewhat simpler life that is less influenced by the big world outside. I should think you might gain a better understanding of the culture and history there if you actually stayed in places that are "Black-Foresty." Freiburg really is a world apart from the Black Forest. The same is true for Baden-Baden (think casinos, spa treatments.) While Freiburg and B-B might be interesting places to visit for some, and while they enjoy prominent space in Rick Steves' less-than-thorough handling of the Black Forest region, I suggest that you find base-town accommodations somewhere else.
Below is a link to Bavaria Ben's webpages for the Black Forest. Ben and his friends/acquaintances have collectively spent thousands of days exploring the Black Forest, and their experiences and finds might be helpful. While the site is dated now, the point of it is to show you the types of places you might stay instead. Some inns/farms/B&B's are likely operational - you might do a search for them.
http://bensbauernhof.org/farmscentralbf.html
main page: http://bensbauernhof.org/index.html
I am on the same page as Lee regarding public transport. Small town size is not an indicator of isolation. I've had a car in the BF (once) and have done multiple visits to different parts of the BF by train. I vastly preferred the rail trips - and the occasional bus trips - I took in connection with those trains worked out just fine too.
The Vogtsbauernhof is a major must-see if you believe in must-sees.
Gengenbach (where you CAN get the KONUS card) is both a charming and effective base town for rail travel, as already mentioned. Nice restaurants there, but look also into Baiersbronn for Michelin-class dining if you're into that. It would be fairly simple to day trip by train from Gengenbach into Freiburg and Baden-Baden (if you have reason to visit those places.)