Berlin Airports - Mitte District
 

What is the easiest and/or most cost effective way to get from Berlin Schoenefeld Airport to the Mitte district? And than the Mitte district to Berlin-Tegel (Otto Lilienthal) Airport (TXL)?

the free bus from shoenefeld takes you to the train station 500 m. away.
they buy a metro ticket or daily pass.

to go to tegel.. wonderful public bus goes right there making several stops all through certain parts of berlin.

they are well marked.

Where are you going in Mitte? As lincasanova mentioned, you can get the train from near Schoenfeld. It makes stops at several stations, and you probably want Friedrichstrasse.

Oranienburger Strasse is the location of the hotel.

It's not too long a walk from Friedrichstrasse to Oranienburger Strasse. Perhaps 500 meters.