We will be visitng friends in Munich, and then heading to Dijon/Beaune in mid-May. Trains are quite expensive, flights non-existent. Help!
Munich to Dijon takes the better part of two days to drive, so I doubt a train link would get you there rapidly. The nearest airports are probably either Geneva or Lyon. Try flying into one of those locations and hopping on a train from there.
The most direct route seems to go through Basel. You can get from Munich to Basel SBB Bahnhof for €39 with an advanced purchase, non-refundable Europa-Spezial Schweiz fare from the Bahn or for €29 from Munich to Basel Bad Bahnhof with a Sparpreis fare.
There are three train stations in Basel. Basel SBB is the main station for Swiss Rail; Basel Bad Bahnhof, although in the Swiss part of Basel and is considered a German Rail border station. Direct trains for Dijon leave from the SBB station. The two stations are a few minutes apart by train, a little longer by streetcar. Bahn Sparpreis tickets will only go to the Basel Bad Bhf; Europa Spezial Tickets will go all of the way to the SBB station, but are €10 more.
By streetcar (#2), it's a 10 minute, 1 zone ride. €3 adults, €2 children.
Besides the route via Basel that Lee described, the DB site also shows a route via Strasbourg that takes about the same amount of time (9 1/2 hours).
Book Munich-Basel or Munich-Strasbourg on the DB site to get the Europa-Spezial Frankreich fare. Book either Basel-Dijon or Strasbourg-Dijon at www.tgv-europe.com. To keep the tgv-europe site in English and to avoid being bumped to the Rail Europe site which doesn't offer discount fares, choose Great Britain as your country of residence.
Book all tickets ASAP to have the best chance of getting discount fares before the allotted number of tickets are sold.
Additional note: It might be wise to buy either Basel-Dijon or Strasbourg-Dijon tickets in Munich, even if you have to pay full fare for them. That way all you won't have to rush to retrieve them from a ticket window and will only have to find your connecting train.