Can anyone remind me as to why Serena is living in the Waldorf penthouse??

Honestly, because the producers don't want to destroy the RIDICULOUS set which is no longer necessary (with Eleanor having moved to Paris and Blair split between the NYU dorms and Chuck's), so they've tried to give it some purpose by moving someone else in.

The show didn't really fully explain why Serena moved in, just threw around a few weak excuses.

In "Dan the fleurette (3x04) Serena moved at the Waldorf penthouse because she fought with her mother and asked Blair if she could stay there. Then when Serena and Blair fought I honestly don't know where Serena was staying. I guess at the Empire since in 3x11 (The tresure of Serena Madre) Chuck mentioned something about Serena staying at his hotel. Finally in 3x13 we saw her again at the Waldorf's. I don't know why, LittleDancer 123 is probably right about her presence there XD

It is because she has fallen out with her mother, because of what she did with her father in the hotel room, also because of the whole trip storyline.