Itinerary from Chambery/Lyon to the Alsace and Black Forest areas

My preference is to stay in mid-sized Colmar and daytrip to Strasbourg or neighboring wine road towns. This forum has several recent discussions about doing that. A couple of early morning bus/train departures from Colmar to Freiburg only take 1.5 hours (compared to 2 - 2.5 hours later in the day), when you're ready to head that direction.

If you're definitely heading north into Germany, then Frankfurt airport is the logical departure point, but if Rothenburg ob der Tauber is not key to the plan, then Basel/Mulhouse/Freiburg airport is an option, just over an hour from Colmar or Freiburg (but always with a connection at Basel to the airport bus). If you are actually sleeping in Strasbourg, then Strasbourg Entzheim airport is only 10 minutes away.

How to Look Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it.

Any previous travel experience will serve you well here, regardless of being in Europe or being alone. Try not to feel nervous. See two articles on tips for solo travel at http://www.ricksteves.com/travel-tips/trip-planning.

A quick look at http://matrix.itasoftware.com/#view-flights:research=DTWGVA-FRADTW
shows best to fly Detroit to Geneva via Washington Dulles and return on a nonstop from Frankfurt, on United and partners.
Geneva has a train station right at the airport to get trains connecting to Chambery via the main Geneva station in about 1 hour 40 minutes.
Chambery to Colmar is about 5 hours at best. The best connection is at 10:42 going to Lyon and then TGV train to Colmar.
From Colmar you can visit surrounding villages. It is an easy bus ride over to Freiburg, then to Frankfurt by train where again, there is a train station right at the airport.
With 5 full days between Colmar, Strasbourg, and Freiburg is really all you have time for. Rothenberg will kill two whole days getting to and from. Skip it this time around. Villages near Colmar, like Turckheim and Kaysersberg are equally cute.

Colmar, Strasbourg, and Freiburg are not villages but towns and cities. As various people have said, Rothenburg is a long way away and not a good use of your time. There are plenty of picturesque small towns in the areas you're already staying in. (Riquewihr is a small town in Alsace that still has intact walls.)

Thanks for both of your suggestions. They're very helpful. Just a couple of follow- up questions... If I use Colmar as a base, would it be easier to fly out of Strasbourg vs. traveling to Frankfurt? Also, if I'm using the links you sent correctly, it looks like the trip from Colmar to Freiburg is about 2 hours. Is that right? I'm wondering if I should spend a night or two in Freiburg as well as Colmar...

The problem with Colmar to Freiburg is a whacking great big river between them. As the crow flies, or the car drives, they are pretty close.

Unfortunately to get between them by train means a long trip north from Colmar to Strasbourg, change onto the dinky little Black Country train to Offenburg, Germany, and then south on a train to Basel; or south from Colmar to Basel SBB in Switzerland, transfer by tram to the Basel Bad Bf German station across the river (still in Basel) and back north again by train on the German side.

Coming back in the evening you do it all again.

I don't know anything about it but I believe that there is a bus between the cities which has to be way faster and easier.

Or stay in the Black Forest as you suggest.

Flying from Strasbourg will involve changing planes somewhere, probably Paris (not fun), or at least Amsterdam. I always prefer flying from major airports, especially if they have nonstops home. Frankfurt fits the bill.
Yes, it is about 1 1/2 hours to Freiburg, on the bus to Breisach, then the train to Freiburg according this schedule: http://www.suedbadenbus.de/suedbadenbus/view/mdb/suedbadenbus/freizeitangebote/pdf/2014/mdb_175908_fly_euregio_2015_web.pdf
I'd stay in Freiburg at least one night. Spend two and take a train or bus into the Black Forest. Then its is a straight shot to Frankfurt on the train.