Our plans are to fly into Stuttgart, stay in the Black Forest area for 7 days, with day trips to Strasbourg, maybe Zurich and to see Dachau. We want to be able to stay in one centrally located town in the Black Forest area, while flying into Suttgart and taking a few day trips from our B&B. We will be using the train system, which I'm completely unfamiliar with. Are we able to go to the train station and buy a through ticket for the above cities without reservations? I thought about staying in the Offenburg area, but if there is another city that would be better for us, please advise. Really we just want this to be a relaxing trip to see the beautiful area of the Black Forest, while taking a few side trips.
You can probably daytrip to Strasbourg, and maybe to Zürich, from one of the Black Forest towns, but Dachau is awfully far; I'd plan to overnight in the area and maybe see something else there too. From Triberg, high in the Black Forest, Strasbourg is 1.5 hours away by train; Zürich is 2-2.5 hours. You can pick other towns that may interest you and find the travel times just like I did at this website: http://reiseauskunft.bahn.de/bin/query.exe/en This is a handy map of southwest Germany that shows how the rail lines run: http://www.bahn.de/regional/view/mdb/pv/planen_buchen/liniennetzkarten/2010/MDB81278-streckenkarte_bawue_09_2010.pdf You might want to locate in one of the towns that offers free travel throughout the Black Forest area for your trips there; use this list: http://www.schwarzwald-tourismus.info/service/konus/was_ist_konus/uebersichtskarte/hier_erhalten_sie_ihre_konus_gaestekarte http://www.blackforest-tourism.com/konus
If you want to travel longer distances cheaply, to Zürich, for example, you should use the rail itinerary site I gave you above to purchase advance-sale discount tickets. I'm traveling from Rottweil to Zürich next month for 19 Euros on such a ticket. These go on sale 92 days in advance of your travel date and are train-specific; changes require extra fees.
A day trip to Dachau is not really possible from the Black Forest in my opinion. A good day out by rail from this area would be the Bodensee. You could take a short boat trip across the lake for lunch.
I'd stay in Freudenstadt. It's really in the Black Forest. It's an easy trip from there down to Baden-Baden or Strasbourg. You could also take the Nagold river route down to Calw, home of Hermann Hesse. A pretty little "avant garde" fachwerk town. For local rail transportation in Germany, I never get reservations. But then, I do most of my travel by regional trains, which don't have reservations.
I'd urge you to stay a few nights in Stuttgart, a great town! Ludwigsburg Palace is easily reachable by train and a great tour. The downtown city park is great, good restaurants, plus museums (Porsche, Mercedes, Stadt, etc.).