"How long are you here for?" is common and natural in BrE.
Suppose this is a dialogue between two people who have just got chatting in a bar in London:
Jane: Hi. I'm Jane. What's your name?
Tara: Hi, Jane. I'm Tara. It's nice to meet you.
Jane: Do you live in London?
Tara: No. I'm just here on holiday.
Jane: How long are you here for?
Tara: Three weeks, then I'll go to Edinburgh for six days and then I go home.
Jane: Great! Where's home?
Tara: New Zealand. How about you? How long are you here for?
Jane: I live here. I've been here for seven years now. I'm actually from Manchester.
Tara: Lucky you! I'd love to live in London. Anyway, I'll probably see you around.
Jane: Yes, I'm here most evenings. See you soon.
Tara: Bye!