Train travel

If you buy the tickets three days before you use them you will get a discount, sometimes as much as fifty per cent. We have done this all over Germany. You will need reserved seats on other than local trains for instance Munich to Cologne. When you walk up to the very helpful ticket counter its a good idea to have printed the name of the town you want to travel to on a piece of paper so the ticket clerk can see it. Its easy for us Americans to not pronounce German towns correctly and may be sold a ticket to somewhere we don't want to go. This has also happened to us in Germany.

Don't rule out other towns such as Ulm.

For "nearby Bavarian towns", there are day passes you can buy on the day of travel for the round trip, from a ticket machine. Depending on your destination, one of several such passes may be useful. They are valid on local/regional trains (RB, RE, and others) not the high-speed trains (IC, ICE, EC for example.) Seats on these trains are not reservable - just purchase and board.

The Regio-ticket Werdenfels costs €20/1 and €6 per additional adult passenger. It's valid for trips between the Munich region and the Garmisch-Mittenwald area. Unlike most day passes, it is valid every hour of the day, any day.

These two are valid after 9 am weekdays, anytime on Sat or Sun:
Bayern Ticket €25 + €6, good for all of Bavaria and Salzburg as well.
Regio-ticket München-Nürnberg (€20 + €6, for Munich-Nuremberg)

You don't need seat reservations on any trains in Germany. However, for the highspeed trains (ICE), which run mostly between large cities, you can save money by buying the tickets in advanced. This, however, is not the same as a seat reservation, which is purchased for a small supplement in addition to the train ticket.

Regional trains do not offer advanced purchase discounts, nor do they have reserved seats. Simply buy your tickets, or one of the many passes known by others much better than I, on the day of travel

Monte, the advance purchase Savings Fare tickets no longer have to be purchased three days in advance, one day is sufficient, although I'm sure it goes by German time. It's already tomorrow in Germany, so you are looking at tickets for Friday.

one day is sufficient

Since dec. 2016, you can buy a Sparpreis ticket even same day if there are seats available, but then the discount won't exceed 8 to 20%, depending on destination. When I returned from the US recently, I looked up the DB App while waiting at the luggage carousel and was able to get a 15% discount for an IC leaving Munich Hbf two hours later.

Thanks for all of the useful information. We appreciate the time.
Linda