From Stuttgart can someone suggest a route for a day trip to the Black forest by train?
It really depends where you want to go in the Black Forest. Are you interested in visiting a particular city like Freiburg or Baden-Baden? Are you looking for a particularly scenic train journey with less of a focus on destination? The most scenic Black Forest rail line does not run directly to Stuttgart - you'd have to catch a train to another city on the route and go from there, which would be a long trip but doable if you're fine with spending most of your time on the train.
Stuttgart isn't an ideal base for an outing into the Black Forest. But there are a few outstanding villages nearby that you might look into. For a short jaunt, attractive Calw is about one hour away; getting there involves a train from Stuttgart to Weil der Stadt, or possibly Böblingen, where you connect to a bus that gets you over the mountains and into Calw. ON a full-day outing, you could also visit Freudenstadt and Schiltach. Schiltach is particularly stunning. You can visit all three places in a sort of loop. From Stuttgart take the direct train south to Freudenstadt at 8:18 or 9:18 and arrive 1 hr. 20 minutes later. Schiltach is less than 30 minutes by direct train south of Freudenstadt. Schiltach to Calw takes 1 hr. 45 min. with changes in Freudenstadt and the tiny station of Hochdorf. Then from Calw, you'd do the bus-train connection back to Stuttgart. A daypass for Baden-Württemberg (the state you're in) costs 29 Euros for 2-5 people, 21 Euros for one: http://www.bahn.com/i/view/USA/en/prices/germany/laender-ticket.shtml
I agree with Russ. I went to Calw in 2008 and was very impressed. Calw, the home town of Hermann Hesse, is an Avant garde little village with lots of fachwerk buildings. If you eschew the bus (and you shouldn't), the train route, via Pforzheim, takes only a little longer.
If you're pressed for time, taking the train from Freiburg to the Tittisee is scenic. Get off, take an electric boat trip on the lake, and back again in time to take the cable to the Freiburg overview noted above. And, time to climb the cathedral tower!