Should I pull for NY!Azura??

You will have her in a legendary banner probably with 8% chance to get a 5*. So you can miss this banner if you want.

Try summoning for her
A flying singer is too good to pass up on
Don't blow all your orbs out though

Okay, I personally pulled for her and she's not bad if given the right IV's (+spd being the best because you avoid doubles). However I can only truly recommend her if you use flier emblem ALOT. Its not like she can't be used outside of it, but she truly shines in Flier Emblem, giving and getting flier buffs. In short, unless you really want a dancer for your flier emblem and you know that you'll use them, then go for it. Otherwise wait for a Legendary Heroes banner

If you're down dancers, you can try for her in no more than 80-100 orbs. Even in a non-flier team, she would have remarkable uses simply because she's a dancer. But if you have regular Azura, Olivia, and Ninian, it may not be as necessary. Besides, pulling on greens during 8% banners is more favorable than pulling on other colors. I wish they overlapped the NY banner with the Legendary banner. What if people get extremely lucky in the 8% banner and want to come back to the NY one?

if you run flier emblem
then sure, go for her
but if only for collection purposes i wouldnt suggest it
the banner may screw your orb count
if you plan on using her, shes worth it
if not, then dont feel pressured to do so

If you want to play it safe wait for the FEH channel later tonight before making a decision. If you absolutely want and need that Azura with no other available options for a Green dancer then commit at the very least 100 orbs to sniping for her right now. Why wait for a legendary banner at the end of the year to release with her that makes it harder for you to pull her.