After playing some games on Syndra yesterday, here are my thoughts:
She's mad fun to play. Setting up Q->E combos for stuns make you feel amazing.
I frequently overestimate the range of my E and mess up Q->E combos.
Gotta level W first, best damage, range & AP ratios.
W is screwy and if you throw minions they won't always explode on impact because they bug with terrain. This bug sorely needs to be fixed for Syndra to be worth anything. I've had many occasions where I Q+E stun, then W->W a minion on them and they leave the area after the minion lands but before it explodes.
She has a good wave clear time that will let her roam and help other lanes.
Her ult requires you to get really close compared to her other abilities so I wouldn't suggest saving it to burst a carry, and instead just use it on whoever wanders too close and shotgun the orbs into their team for AOE stun. Would also not suggest going for a 6-7 orbs until you feel more comfortable with Syndra's kit.
Her AP ratios really kinda suck so my build has been pure armor pen and CDR. Sorc shoes, DFG, Athene's, Abyssal, Void Staff, & Zhonya's in no particular order.
Laning-wise, she has really good range + harass with her W. It's like Galio's Q but buggy. She also probably can't guarantee a burst until the enemy is sub 50% hp, unlike other burst carries that will do from 75%+.