It's a 10 leave in hair product
maybelline BabyLips
Cozy PJs
Fuzzy PJ shorts
Fuzzy socks
A beanie from Urban Outfitters
philosophy products
Starbucks gift card
Suave Dry Shampoo and conditioner
Nordstroms BP infinity scarf

I think there is still time to do that - ask your teen daughter to register on wanelo.com and make a huge wish list (there are many trendy things posted there to choose from plus she can add stuff from all over the whole Internet), stuff you would not believe exists! Then you can surprise her from a few items from her collection. My daughter made a huge wish list so she probably does not even remember what she posted and I am getting a couple of inexpensive things from it (like a funny cat hoodie and an etsy iPhone case).

book store gift store- Politics & Prose if she is in the district. Are there restaurants near her school- gift cards are always great so they don't have to ask mom for money. Also movie gift cards are great for this age.

Love all of the above suggestions. My 13 yo DD would also be happy with flannel or fluffy pj pants, a fleece hoodie.

If she's a girly girl - go with the nail stuff or perfumes

My girl is still silly and fun (vs. "mature") and would like funky socks, those animal winter hats, fun pens and markers (she and her friends decorate everything with Sharpies!)

Can't go wrong with iTunes or movie theater cards.

Scarf and gloves/hat set
cute sweater
gift cards
movie tickets
cute inexpensive purse or wristlet (got one of these for my 14 yo baby cousin and it was a hit)!

Any accessory. Girls love accessories, even if they aren't expensive. Just try to get something that looks like it is aimed at younger women (usually sparkly or shiny)

Aa an... Pink... I HATE that place.

I have a few 14 yo nieces that requested:

Make up
Earrings
iTunes gift card
PINK gift card

All in that range..

...more please! My 13 year old has a lot of stuff, and what she asks for is expensive. (coats, shoes etc) Something fun! and +1 on the pillow pet.

BP Nordstrom carries cool accessories for around and under 20 bucks like iPhone cases, makeup bags, scarves, lip gloss and nail polish sets.
I have a 14 yo DD too and it's maddening to find something for her because she already has a shitload of everything. Urban outfitters is the new fad for her and they also carry a lot of small crap like jewelry and hair products that the girls like.

Taylor Swift perfume

I'll endorse the PP's suggestions (some of those items appear on my daughter's list right now, actually), and add:

sterling silver earrings or pendant

jewelry holder (Container Store)

gift card - iTunes, Starbucks, Spotify, Barnes & Noble, Claire's

socks - fuzzy or holiday

mug - my daughter's 15 and she & her friends like tea

a gift pack of those Philosophy shower washes or lip glosses

pillow pet (really)

Does she have an iPad? Maybe a stylus?

Sephora gift card?

I am completely lost!!
I know when I was that age I would have liked a latch hook or macrame kit, but times are a changin' and I am old.
Need under $20 gift ideas.

Much thanks in advance.