Day trips out of Munich

Augsburg is half an hour by train.
Nurenburg is about an hour by train.
Salzburg, Austria and Berchtesgaden, Germany are worth more than a day trip, but you can do them on day trips.
Garmisch, Fussen, Oberammergau are great and you can spend more than a day there, but also can do day trips there.
Regensberg is a couple of hours by train and worth a trip.

Dachau Concentration camp is just North of Munich.

Doing the Romantic Road is more than a day trip, but you can get tours from Munich.

I would suggest Ulm, Augsburg, Ingolstadt, and Regensburg..."...the best." That depends on what you're after as regards to specific interests.

• Andechs Monastery & Brewery
• Tegernsee
• Ettal monastery & Linderhof Palace

I'm not sure I really understand your question. Germany in general, and Bavaria specifically, is an area rich in public transportation possibilities. All the places mentioned above are readily accessible by train or by train and public bus, so why do you seem to focus on "tour bus day trips"? For the most part third party tours just add cost to what you can easily do yourself.

For a lot of trips in Bavaria, a Bayern-Ticket (31€ for 2 people) will provide you with unlimited trains and bus use for an entire day. You can go almost anywhere - Füssen and the castles, Oberammergau and Linderhof, Salzburg, Regensburg, Nuernberg, Mittenwald, etc. Dachau is a Munich suburb and a local ticket will do.

You may also want to see Munich:
Discover Munich from different perspectives

Tours guided by night watchmen or chambermaids, in a stretched limousine or by Segway give you different impressions of Munich, a city with many different faces.

These tours may be fine, but I'd probably go with a less gimmicky tour.