There are two different ticket types you can buy to travel to go sight-seeing on public transport in Munich:

 MVV Automat      

You can buy both types of tickets from all MVV ticket machines or the manned counters.

 

The CityTourCard is more expensive than the MVV ticket, but it may pay off for you if you plan on visiting many of the sights for which it offers discounts.  Depending on the sights you want to see, you would have to do your own calculation of:


total cost

= transportation + entry fees - discounts

 

See here for a flyer (7.5MB) explaining how to get to several sights with public transport.

map of all U-Bahn (subway) and S-Bahn lines (1.09 MB): http://tinyurl.com/munich-metro2013

map of all tram lines (170 KB): http://tinyurl.com/munich-tram2012

If you use a bus or a tram you will get to see more of Munich, since they run above the ground, while the U-Bahn and S-Bahn are underground.

Remember, with your public transport day tickets (MVV or CityTourCard) you can get on and off any bus, tram, U-Bahn or S-Bahn, so they are just like a hop-on/hop-off tour.

 

Marienplatz

The Marienplatz is the centre of Munich's historic city, with the Rathaus, its Glockenspiel (at 11am and noon, as well as at 5pm from March to October).
Take the lift up to the top of the Rathaus and see Munich from above (open Monday to Friday 10am to 5pm, until 7pm from May to October). 

The Marienplatz is also the centre of Munich's pedestrian zone with all the shops.

Marienplatz Munich    

 

Viktualienmarkt

It's just 200m south from Marienplatz to the Viktualienmarkt, Munich's farm market. Open Monday to Saturday from 8am to 7pm.
Browse and buy whatever you want from the many market stands and then picnic at the beer garden in the centre of the Viktualienmarkt, the locals do it, too!

Viktualienmarkt Munich

 

Hofbräuhaus

Munich's best known beer hall, with loud, cheerfull live Bavarian music. The Hofbräuhaus was built in 1589 and hasn't had a quiet day since. 200m east of the Marienplatz.

Hofbräuhaus Munich

 

Dallmayr

Dallmayr is over 300 years old, was purveyor to the Bavarian kings and is one of the two rivals for the title of best delicatessen store in Munich. Has a café (open Mo-Sa 9:30am to 7pm, breakfast until noon) and a restaurant with 2 Michelin stars upstairs from the ground floor delicatessen store. 
Located between Marienplatz and Odeonsplatz.

Dallmayr Munich Dallmayr interior Munich

 

Zoo

To visit the Hellabrunn Zoo, you can either take the U-Bahn line U3 from Marienplatz or "Sendlinger Tor", or the bus line 52 from Marienplatz or Viktualienmarkt to the stop "Tierpark" (= zoo).

Both run every 10 minutes, the U-Bahn takes 9 minutes, the bus 18 minutes.  

       Icebear Hellabrunn zoo
 

 

Nymphenburg Palace and Park

To visit the Nymphenburg palace, you can use the tram 17.
Get on at "Sendlinger Tor" or "Karlsplatz" or "Hauptbahnhof" and get off at "Schloss Nymphenburg".
There's a tram every 10 minutes and the trip will take about 18 minutes.

Nymphenburg Palace

 

Olympic grounds

The Olympic grounds from the 1972 Olympics with the Olympic stadium, Olypmpic park and Olympic TV tower (has a lift and excellent views of the Alps for 4.50€ and 1€ discount if you also have ticket to BMW Welt or Sea Life) housing a Michelin-starred restaurant, Sea Life and BMW Welt near-by are located near the metro stop "Olympiazentrum" on the orange U3 U-Bahn line, see here for a map.

Olympic stadium Munich

 

Museums

If you want to visit the Pinakotheken museums: http://www.pinakothek.de/  the nearest public transport stop would be the stop "Pinakotheken" on the orange tram line 27 (you can take it from the stops Karlsplatz or "Sendlinger Tor").

Alte Pinakotek:  14th to 18th century paintings by Leonardo da Vinci, Raffael, Rembrandt, Rubens, Dürer, Titian, Boucher, ...

Alte Pinakothek Munich      

Neue Pinakothek: 19th century paintings by van Gogh, Monet , Cézanne, Gauguin, Toulouse-Lautrec, and many more as well as sculptures by Rodin, Thorvaldsen, ... 

Neue Pinakothek Munich     

Pinakothek der Moderne: modern art, by Matisse, Picasso, Marc, Kirchner, Dalí, Miró, Warhol, ...

Pinakothek der Moderne     

Brandhorst collection: modern and contemporary art by Warhol, Twombly, Hirst, ...

Brandhorst collection     

Residenz-Museum, Treasury: residence of Bavaria's kings, largest city palace in Germany. Don't miss the adjacent royal gardens, the Hofgarten. Near stop "Odeonsplatz".

Residenz Munich     Kaisersaal    Hofgarten

Käfer: not a museum but Dallmayr's rival for the title of best delicatessen store in Munich and well worth a visit. Near bus 100 stop "Friedensengel / Villa Stuck" or U-Bahn stop "Prinzregentenplatz".
Feinkost Käfer     Käfer's cake department

You can also use the public bus line 100, which is also called the "Museum Bus" to visit the museums, it stops at 21 museums.
See here for an overview of museums on the route.

You can get on the bus 100 at Hauptbahnhof (= in front of central train station) and there's one every 10 minutes.

Bus 100 at the stop Odeonsplatz:
MVV Museum bus line 100 at stop Odeonsplatz  

photo of a Munich tram:
 MVV TRam

and what the inside of the tram looks like:
MVV tram inside