The Black Forest runs about 160 km north to south with no single centre, so the town you pick decides the holiday: a city with trains, a lake with lifts, a railway town in the middle, or a spa town at the far northern end.
Freiburg im Breisgau — the city base
The only real city on the western edge, with trams, an old town threaded by the Bächle water channels, the Münster, and the Schauinsland cable car on its doorstep. Gives you restaurants and rail connections at night and mountains by day, plus easy trips to the Kaiserstuhl vineyards, Alsace and Basel. Weakest for actual snow — the city sits on the Rhine plain.
Titisee-Neustadt — lake, lifts and the Höllentalbahn
Half an hour from Freiburg on the Höllental railway, in the middle of the Hochschwarzwald. Puts the Feldberg ski area, Schluchsee, the Wutach gorge and the Badeparadies waterpark within reach, and the Hochfirstschanze ski jump is in the town. Titisee's lakefront is built for day-trippers; Neustadt, the other half, is plainer and cheaper.
Triberg — the middle of the forest, on the Schwarzwaldbahn
A small town wrapped around Germany's highest waterfalls, on the Schwarzwaldbahn between Offenburg and Konstanz, which makes it one of the easiest bases to reach without a car. It is the cuckoo-clock centre of the region and the closest practical base for the Vogtsbauernhof open-air museum at Gutach. Expect very little open after 21:00.
Baden-Baden — the spa end, with a caveat
The northern tip: twelve thermal springs, the Friedrichsbad and Caracalla Spa, the casino, Lichtentaler Allee, the Festspielhaus and the Iffezheim racecourse nearby. Practical tip — it is a fast ICE stop and the start of the Schwarzwaldhochstraße, but it is a long way from Feldberg and Titisee, so treat it as its own trip rather than a base for the southern forest.