This is the zone map of Munich Metro (MVV). The centermost, M zone (in white), is where just about everything most people want to see, except for Dachau, is. Dachau is in the next zone out from M, Zone '1'.
This is the table for fares in the MVV. A Group Day-ticket allows you (2-5 people) unlimited use of all of the means of transport in that zone of the MVV (S-/U-Bahn, streetcars, and bus) for an entire day, until 6 am the following morning. The M zone day-ticket for the central zone is 15,60€. For M-1 (central, M, zone and the next zone) is 17.-€.
On your first day, since you say you are staying near the Hbf, you might want to forego a ticket and just walk to Marienplatz, enjoying the shops on the pedestrian only Kaufstrasse, watch the Glockenspiel do it's thing in Marienplatz at 11am, just sit in Marienplatz watching the people and the mimes, have lunch at Hofbräuhaus, or tour the Residenz. The Deutsches Museum is an interesting place and not to far a walk from Marienplatz. Or you can use the 15,60€ M ticket and take the S-Bahn or streetcars to go everywhere, whatever.
If later you want to go out to Nymphenburg, the M ticket will take you there. You can catch the #17 streetcar to Nymphenburg from the north side of the Hbf (Arnulfstrasse).
If you want to do Dachau, buy the 17€ M-1 day-ticket and take the S2 S-Bahn (direction Petershausen) to the Dachau Bahnhof ant the 726 bus from in front of the Bahnhof 7 minutes to the K- Z Gedenkstätte "Memorial".