German Unity Day in Bavaria

Oktoberfest normally ends on the first Sunday in October. However, if the first Sunday comes before the Day of German Unity, Oktoberfest ends on that day instead.

Are there any events in the area that would be fun to see?

Not at all. Some politicians will gather somewhere and repeat the same phrases as every year, but this will go largely unnoticed by the public. No more traffic in Andechs than on an ordinary Sunday.

In Frankfurt, they have "Jazz on the Römer" which is the old town square every year, with tables and benches set up. It is a nice party, like a fest.
Of course this is not in Bavaria, but wanted to counter the comments that nothing happens in Germany.

It is not a jazz festival. It is a festival to celebrate Unification Day, and am sure there will be some speeches.
We have Jazz festivals at other times.

Germans are a bit allergic to patriotism.

For example: If I see too many German flags in a neighbourhood or village, and it is not time for a national Football match, I am slightly concerned.

Oct. 3rd is recognised in official, formal contexts, and sometimes with cultural or so events, but not so much beyond that--there aren't lots of informal family gatherings or so, as in many other countries on equivalent national holidays. It is a bank holiday, though.

A brief postscript that contextualises our discomfort with patriotism: The most natural choice for a commemoration day for German reunification would be November 9th, as that was the day the Berlin Wall fell. However, since that day (a fateful day in German history) marks among other things some of the worst pogroms in 1938 -- the November pogroms -- we obviously do not celebrate reunification on this day. Further sidenote, while looking up the word for these Pogroms in English, I was somewhat shocked to learn that the word "Kristallnacht" is still used in English-speaking contexts to describe this event. It is viewed as an outdated and fully unacceptable euphemism here.