We fly into Tegel airport. I know we can catch a bus into the city but after 24 hours in the air from Melbourne we will probably want to get to our apartment quickly. Does anyone have any idea how much a taxi will cost?
This is really an answer to your question. You can take the bus from Tegel to Berlin Hauptbahnhof. (main train station). Change to a taxi there for going to the hotel. In which district is the hotel?
Taxi sounds like the way to go for four people. The cost estimate in Rick's Berlin chapter is similar to George's - about 15 euros from Tegel to Bahnhof Zoo or 25 to Alexanderplatz, including the .50 airport fee.