Wouldn't bother with a taxi - the S-Bahn is quick and efficient (unless you have lots of bags). S1 faster to the west side of the city, S8 faster to the east side, though not much of a difference if going to Hbf/Karlsplatz-Stachus/Marienplatz.

An all-day all-zone ticket is something like 12 eur (someone please correct me on this).

The Lufthansa airport bus runs from the airport to the Hauptbahnhof, picking up across the street from the Eden Hotel Wolff. Dunno on pricing, but schedule-wise I believe it's pretty close to the S-Bahn in terms of time.

Only word of caution would be that the last time I rode the S-Bahn (S1 if it matters), it split into two trains at one stop, with the front half going elsewhere and the back half going to the airport. Most (if not all) of the announcements were in German, so those who speak none might be caught off-guard and end up somewhere they didn't want to be...