Marienplatz is not only the center of the old city, but also the place where two of its metro lines (U-Bahn) and seven of its commuter trains (S-bahn) converge.
I recommend moving around Munich in public transport. You can buy a one-day or a one-week ticket, which gives you access to all local transport (metro, trams and buses) in a given area.
Also recommended is the Munich City Tour Card, which gives you access to transport services and a discount for tourist attractions. There are single tickets or group tickets (for up to 5 people) valid for one or three days.
In the picture you have one of the statues in Marienplatz.