Germany 6 Days in November

"Are we better to buy a Eurail Pass..."

Those are for Europe. There are German Rail passes as well but since you'll only be in Bavaria, use the Bavaria Ticket - €28 for two per day, purchase at a ticket machine as you go, details here:

http://www.munich-touristinfo.de/Bavaria-Ticket.htm

You may find that the cheaper Regio-ticket Werdenfels pass, valid in a smaller zone within Bavaria, is good for certain routes:

http://www.gapa.de/blobs/flyer_tickets_werdenfels_en.pdf
http://www.bahn.de/regional/view/mdb/pv/deutschland_erleben/bayern/regionales/regio-_u_hopper-tickets/dez_2014/mdb_175946_rt_werdenfels_karte_dez_2014.pdf

"Is it realistic to think that a trip to a city like Cologne, Dresden or Berlin is doable in addition to Bavaria"
No. But there are some excellent, good-sized Bavarian cities to consider instead. In no particular order:
Bamberg
Würzburg
Augsburg
Regensburg
Nuremberg

We do not ski, but love to hike, so something active in that regard would be great.

Hiking options in the Alps are fairly limited in November, because this is a transitional period where there isn't enough snow to ski, but the enough to block the trails at higher elevations. You could try the Partnachklamm (a gorge) in Garmisch-Partenkirchen. You could also try hiking elsewhere in Bavaria. The lower elevation mountain ranges, like the Spessart, Bayerischer and Oberpfalzerwald should be (mosty) snow-free in November. My only experience in hiking outside of the Alps in Bavaria, though, is in the Fränkischer Schweiz (Franconian Switzerland) region northeast of Nürnberg, but it would be all but impossible to reach the trail heads here without a rental car.

Agree with Russ, with only 6 days, you really don't have time for Berlin, Cologne or Berlin.

If you could get a VRBO in Munich close to a transit line for the week, you'd have plenty to do for 6 days. 28 euro per day is about the maximum you need to spend for day trips, and that includes Salzburg.
Nuermberg is also an excellent day trip for a larger city. Munich itself could keep you busy for 3 full days. Garmisch-Partenkirchen and Oberammergau for Alps.
Rail schematic:
http://bahnland-bayern.de/tl_files/bahnland-bayern/files/BEG_GR_Streckennetz_SCHEMATISCH_06_2015.pdf

When in particular in November? I ask as the Christmas markets in Salzburg and Innsbruck open mid November this year. We visited them in late Nov. and early Dec. 2010 and 2013.

http://www.salzburg.info/en/art_culture/advent_new_years_eve/advent_christmas_markets/salzburg_christkindlmarkt

http://www.innsbruck.info/en/experience/events/detail/article/christkindlmaerkte.html

Our pics:
www.flickr.com/photos/pjbassplyr/sets

Paul

My wife and I are not hikers but avid walkers. German cities are a joy for their extensive pedestrian zones and many walkways. The list of towns that Russ gave are all good for walking. Regensburg and Würzburg have green belts around the city centers where the the town walls used to be. They are a pleasant way to get to the sights of the town. There is a nice walk up to the Würzburg Marienberg (fortress) across the river and another up to the Käppele pilgrimage church.

https://mcchelsea.smugmug.com/Travel/Empty

I might add Landshut to the list for its walk through the old town and up to its castle, circle back through the castle grounds for good views of the city from above.

https://mcchelsea.smugmug.com/Christmas-Markets-2009/Landshut-2009

If you head to Bamberg, take a walk unto the grounds of St. Michaels.

https://mcchelsea.smugmug.com/Other-2/Bamburg-2014

Würzburg, Regensburg and Bamberg would be my three favorites for places to stay. We prefer going and staying rather than day-tripping but lots of folks prefer not to change rooms. The Bayern Ticket is a bargain to all of these towns.

There are a few interesting larger cities in Bavaria (Augsburg, Munich, Regensburg, Nürnberg, Würzburg, et al), plus some cities on the borders (Salzburg, Ulm) and a plethora of smaller towns. There is soooo much to see; you don't need to leave Bavaria. You can get everywhere on regional trains with Bayern-Tickets. You don't need a rail pass.

Don't bother with big booking websites that only lead you to expensive accommodations. Use the town websites, www dot town name dot de, and find small family run pensions and private homes. You'll get a much richer experience and save money.

As mentioned, cities like Cologne, Dresden, and Berlin take to long to get to. Focus on Southern Germany.

I agree with Lee about using town websites to find a place to stay. Most of the places I have stayed are not listed on the booking sites and they have been excellent.

Since your wife is a huge Sound of Music fan, I would stay two nights in Salzburg.

I would base myself in Munich for the entire time and take day trips to all the wonderful places everyone else has already mentioned. That would save you all the travel and relocation time between places ... and as you say, you have so many options with Munich as a base that you won't run out of things to do. If you go this route, you can pick your sightseeing (i.e. city vs. countryside) based on the weather each day.

In my opinion, whether you choose to use a site like VRBO/HomeAway to rent an apartment or go with a Gasthaus or hotel is really a matter of personal choice. All are good options with pros and cons. In an apartment you will have to prepare your own breakfast or go out to get it yourself, no one will be making your beds or changing your towels, you will have to take the garbage out yourself, you likely own't have anyone on site to ask questions if you have them, etc. Then again, you will likely have more space, can make yourself a coffee anytime you feel like it, may find yourself living more like a local in a more residential area, can often get better prices in more central locations, etc. You get my point.

In addition to everything already mentioned, a fun 'hike' might be to take the S-Bahn (the suburban rapid transit train) to Herrsching and then walk up to Kloster Andechs and get a meal at the Biergarten.

Bear in mind that the weather in November can be very cool, damp and changeable. You may find that you want to be focusing your itinerary more on activities that allow you to get in out of the dampness more frequently than you might otherwise.

Salzburg - we stayed in a convent within walking distance of the main square. Bought snack foods at open farmer's market and sat on our window ledge, overlooking quiet courtyard. Loved it. Don't remember the name but it was reasonable and away from the maddening crowds.

As mentioned earlier, the Christmas Market timing would be great. While many start late in the month, there are some that start earlier (middle of the month timeframe). Munich's is terrific..I kept my hot chocolate mug from my last visit. Christmas treats and holiday gifts as far as the eye can see. While I enjoyed Munich's, I have been told that Nuremburg's and others in the area are even better. Even without the Christmas Market possibility, Munich and Bavaria will not let you down. Enjoy!!!

Thanks to all of those who have taken the time to comment so far. So helpful and hoping it will benefit others as well.

Mike