Trians in Germany
 

My husband and I are trying to go from FRA to either Hof or Chemnitz on 30 Nov 07.I have looked at the train fares from FRA to either destination on the bahn.de site. It appears that the fare is 79 Euros per person. Is there a less expensive way to go? Thanks

Here's a less expensive way to go from Frankfurt HBF to Hof HBF if you can be bothered:
Catch a train from Frankfurt, which is in the state of Hessen, to Aschaffenburg, which is in the state of Bavaria. The trip lasts about one hour, and costs about €10-14 per person, second class. There are many trains on this route: One leaves at 0806, arrives at Darmstadt at 0825. You change trains here, catching the 0832 which arrives at Acshaffenburg at 0912.
Aschaffenburg and Hof are both in the state of Bavaria, so at Aschaffenburg you can buy from a ticket machine a 'Bayern Ticket', which costs €27, and will allow both of you to travel for that price. (The Bayern Ticket covers up to 5 people travelling together.)
You can catch a train leaving Aschaffenburg at 0917, arriving at Wuerzburg at 1024. Here you change trains, and get the 1036 to Hof, arriving at 1321. The Bayern Ticket is not available to Chemnitz because that city is in the state of Saxony.
The total cost of your tickets would be €27 for the Bayern Ticket, plus about €14 each for the first stage, a total of €55. Note that the Bayern Ticket does not allow for travel on ICE or IC trains: however the Regional trains are quite quick and very frequent, certainly at least hourly.

There are many ways to save money on German Rail fares. Unfortunately some of them are promotional fares, that allow you to use fast express trains but require a commitment to a specific train. Those include the Dauer Spezial fare, which could be as low as €29 per person. I think the "Dauer" fares at that price are sold out but you might find €49 fares. Even if you are not returning, you can always book it as a RT SparPreis fare at €115,50 (about €58 per person one way). As I said though, these fare require a specific train and if your flight is too late you lose you place and your non-refundable fare.

If you are willing to spend a little more time getting there, regional fares are less than express fares, and using regional trains, you can save even more using Länder-Tickets. For instance, you could each buy a €6,60 ticket from the airport to Kahl, and from there share a Bayern-Ticket for €27 to Hof. That's about €20 per person. I don't know the routing to Chemnitz. You might be able to use a regional ticket to the first stop in Thüringen, then a Thüringen-Ticket (which covers Thüringen, Sachsen, and Sachsen-Anhalt) for €26. Worst case you might need a regional ticket to Kahl, a €27 Bayern-Ticket to somewhere near the Bavarian-Sachsen border, then either a regional ticket or a Sachsen-Ticket for €26 from there. The price of a Bayern-, Thürigen-, or Sachsen-Ticket covers 2-5 people.

You can rent a car for about 4100 US and drop it off.

I would not recommend that anyone rent a car and drive on the day they arrive in Germany. Not with jetlag. I have fallen asleep on several occasions on the train; I am so grateful I was not driving.

My pricing should have been $100 US.

As for the prior posters comment about driving on the day of arrival. I think everyone is in a position to decide for themselves whether they feel capable of driving on the day of arrival. I do it all the time and have never had a problem.

The OP also does not state that they are arriving in Frankfurt from an overnight flight so concern over jetlag may be irrelevant.