Freiburg is the natural base for the southern Black Forest. The wine villages of the Kaiserstuhl — an extinct volcano west of town — are a half-hour drive or train ride and produce some of Germany's best Pinot Noir. The Black Forest proper rises immediately east of the city: the Schauinsland summit, the Titisee lake, and the Höllental valley are all within an hour.
Cross-border trips are easy. Basel in Switzerland is forty minutes by train; Strasbourg in France an hour and a half. Both make easy day visits, although Strasbourg deserves an overnight if you can spare it. The little town of Colmar in Alsace, with its Grünewald altarpiece, is also reachable on a day return.