You may wish to consider the Econtel. It is reasonable priced (70 Euro), connected to TXL via the X9 Express bus which stops every 10 minutes directly in front the hotel (Stop: Quedlinburgerstraße, Ticket 2,10 Euro) and takes 10 minutes to the airport and 10 minutes in the other direction to downtown Bahnhof Zoo and Ku-Damm. For a quick sightseeing, Charlottenburg Castle, one of the very best Berlin palaces, is in 5 minutes walking distance. No need for any taxi (which should be aroung 10 Euro from TXL to the hotel).

Thanks to everyone who posted a response and advised that my parents get a hotel room for their 12-hour layover at Tegel Airport. I was surprised to find out that this airport actually closes at night... It would have been a disaster if they got there expecting to stay at the airport and got kicked out by security and stranded without a room... I've never heard of an airport closing overnight, but as far as my parents not wanting to stay at a hotel it is not because of the expense... They are just afraid of not finding their way around and not making it to their flight in the morning. They do not know German or English and have never travelled much... I guess at this point it doesn't sound like they have a choice though, so I will have to convince them to get a room. I'll probably try to reserve a room for them at the hotels in immediate vicinity to the airport so that they can take an airport shuttle or a taxi. Hopefully it will be a smooth layover and thanks again for everyone's advice!

*think* no english but they want to go to new york? strange.

what you can do to help them - make a phrase book with the most common things on in in english / your language. i would at least give them a crash course in airport english.

for germany they do not need much more to understand than just the taxi sign and how to say "taxi?" and follow them, get into the car and say the name of the hotel.

they should also use a printed out paper in bigger letters with the address of the hotel on it, that will help the taxi driver in case.

berlin has a rather small airport and there is no reason to keep it up at night as there is no activity - why do so?

but it should be a rather easy airport - but new york is quite a different thing ...

Actually that doesn't seem strange to me at all. They may be going to visit family or friends where there will be no language barrier. New York has many ethnic communities; in fact I've read that a greater number of the world's languages are spoken at home by New Yorkers than by residents of any other city in the world.