Strasbourg is an easy daytrip from Offenburg. Daytrips into the Black Forest by train along the scenic Black Forest Railway line are easy as well. In addition to the towns named on the page below, there are 3 other place on or near this line that are worth seeing in the links thereafter.

http://www.black-forest-travel.com/places-of-interest/black-forest-railway.html

Gengenbach: http://www.stadt-gengenbach.de/en/tourism/old-town/

Vogtsbauernhof museum near Hausach: http://www.black-forest-travel.com/places-of-interest/vogtsbauernhof.html

Schiltach: http://www.black-forest-travel.com/schiltach/

Haslach: http://www.black-forest-travel.com/haslach/

The Baden-Württemberg ticket is a daypass that gets you to these places and beyond (Freiburg, for example) for a fixed price:

http://www.bahn.com/i/view/GBR/en/prices/germany/laender-ticket.shtml

Thanks for the suggestions. I had read that the Black Forest area was beautiful. This info will help me narrow down the choices and direction. Is Frankfurt the best airport to fly in and out of?

"Is Frankfurt the best airport to fly in and out of?"

Yes, FRA is probably the best major airport. It's about 1 hr 35 min. from there to O'burg. Regular fare is 53€ on the fast trains. Two can travel on the regional trains for about half that much or less using a group daypass - but the trip takes more than 3 hours on those trains.

For me, which airport depends on the airfare as well. Airfares can vary a LOT. If you get a great deal into Zurich, you might have to travel an extra hour or so and pay more for the train ride, but it might be worth it.

We stayed in Offenburg in Oct. 2011. For us, this was was perfect: a small town , with very good rail links to airport and for day trips, close enough to the sightseeing we planed to visit.

We could visit very easy by train Strasbourg, Colmar, Freiburg, Konstanz, Baden-Baden, Titisee, the fall in Triberg, picturesque small towns Rottweil, Gengenbach.

We stayed at Hotel Central - very well located in the center and near the train station, great room, breakfast buffet very good.

Then we rent a car for some days, and moved to Hechingen, as from there was easier to visit some castles: Hohenzollern , Ludwigsburg and Sigmaringen castle. I think that you can reach these places from Offenburg by train also, but probably there will be long rides.
We love the castles: Hohenzollern is beautifully situated on top of the rock, there's a splendid view of around.
Ludwigsburg is enormous.We visit the "only" about 70 rooms, the tour is 90 minutes and you receive very interesting information so about the history of the place.
Sigmaringen castle is located in the heart of a nice town on a hill above the Danube. Especially impressive are here hunting trophies.
For us, as people born in Romania, we were especially interested in Sigmaringen and Hohenzollern, because Romanian kings were part of the Hohenzollern dynasty.

The train tickets were not cheap enough, at the train station desk they gave us (for 2 or 4 of us) the best train tickets, depend on our destination (there are family tickets, tickets for unlimited rides in one day, etc). Just tell them what you want to do and you will receive the cheapest ticket.

From / to Frankfurt airport, check the time table, as there are direct trains (and this is better when you have luggage) and there are other trains where you have to change.

"Should we fly into Amsterdam and leave from Frankfurt? Not sure if we should rent a car or stick with trains. Looks like it's much more expensive if you rent from one location and return at another."

Yes, it's pricey to drop in a different country. Assuming that you plan to fly into A'dam to actually visit A'dam for a couple of days, it seems like a good idea to fly in there. There's a lot to see there. Getting to Offenburg from A'dam is a lengthy trip - 6 hours driving time if traffic isn't a problem. Travel time is about the same for most trips. Regular fares are quite stiff, but savings fares from the German railways site are as low as 39€ per person - IF you buy well in advance and lock in travel on specific trains. The lowest fares are available 92 days in advance. That means right now, you can buy (or in your case check) tickets for April 27 trains. But you'll have to wait 3 more months to buy your tickets. Be sure to buy them on the very first day they're available for the best selection and prices.

http://reiseauskunft.bahn.de/bin/query.exe/en

Castles: Offenburg isn't exactly a good place for castle hunting. Each of the castles Valtor has suggested is pretty far from Offenburg and will require 4 hours of driving round trip from Offenburg, longer if you take the train. So you might want to see a castle or two in the Middle Rhine Valley as you travel from A'dam to Offenburg.

Marksburg Castle in Braubach has tours all day long and is easy to reach:

http://www.roadstoruins.com/marksburg.htm
www.marksburg.de

A quick stop on the way to Offenburg is possible - but spending a night there would be best - there's more to see than just Marksburg:

http://www.welterbe-mittelrheintal.de/index.php?id=288&L=3
http://www.welterbe-mittelrheintal.de/index.php?id=274&L=3

Use the German railways itinerary page above; click on "change other data" and schedule "Braubach" as a stopover for maybe 2-3 hours to see train schedules. This isn't the fastest route between A'dam and Offenburg but if you take it, your train will pass 40 castles in about 40 miles as you travel between Koblenz and Bingen.