You'll want more batteries for sure. You'll probably also want a nicer charger so you can store your batteries after use and so you can charge more at once. I've been happy with this charger and a parallel breakout board. Whichever charger you end up with, make sure it says "LiHV" and not just "LiPo" so you get one that supports 4.3v high voltage LiPos and not just the standard 4.2v.

Go ahead and buy some spare props, too. The one thing I don't like about my Tinyhawk II is that the props fly off easily in a crash.