I normally use dumbbells for bicep curls. But I will be visiting New York for 7-10 days and I won't have access to a gym so I've been looking up exercises for the muscles I train, like push-ups and things that you don't need equipment for. But I can't find these for biceps - are there any?
This trip is in about a month, so I have plenty of time.

chin-ups

Thanks, I guess that is a bodyweight one but I'm not sure where I'd "chin" myself up from

Bands are easier to pack. I like playing with them once in a while.

I think there's even a workout for bands 'stickied' somewhere.

I just read the sticky (guess I should have looked around first). It seems very convenient - I might get some.

Oh Mongoose, don't feel badly for missing a sticky. This place is huge!

You can do self-resistance bicep curls and isometric bicep curl holds.
Curl your fist on your right hand and resist it by pushing down on your fist with your left hand.
You can do a version of a chin up/pull up with a towel draped over the top of a door.
You can also try "virtual resistance training" where you visualize you're lifting a 100 lb dumbbell (or bigger!) and go through the motion of the bicep curl, but really concentrate and contract the muscle.
One of my favorites is the one arm chin done as a DVR (dynamic visualized resistance).
Here's a demo: http://www.transformetrics.com/content/one-armed-chin-0
As you bring the arm down, you are contracting the muscle as hard as you can. It really works

Best wishes

Another vote for stretchie bands. I love to take mine when I travel. They take up almost no space, and you can vary the resistance just by changing how much band you grab (shorter or longer).

Wow... Some good ideas there - thanks.