So, you like generalist champions, eh? I heard Lee Sin fits well in that category. He's good at helping/saving allies, he has strong gank potential, he has a fair bit of useful CC and his power as a fighter shouldn't be underestimated either. Of course, he doesn't have a particularly powerful ranged-game, but still. Some trade-offs must exist. Not to mention, he's a bit confusing at first and is hard to master, but he can be damn strong if used right.
You could also try Karma or Sona. They're versatile in that they can both be powerful mages as well as great supports. While they aren't as versatile as Nidalee, the simple truth is few champions are. Each of the two have advantages though.
Karma makes a better AP Bruiser than Sona, and can generally hold her own better than Sona too. Through R+W, Karma can heal herself for 20% of her missing health twice, if you use its whole duration. Karma also has a stronger burst of speed on her E than Sona, not to mention it's also her shield, so she can survive even top lane. The fact that Karma has her ult at level 1 also gives her a massive early advantage, which is very useful in any of the lanes.
Sona on the other hand has stronger damage as a mage, but is also squishier. Sure, Sona has a heal that gives a shield, but it's mana intensive to use and the shield is pitiful compared to Karma's. Sona can heal, buff and shield her allies as well though, without the use if her ult. As such, Sona makes a more powerful support.
(If they hadn't been mentioned already, I would also have recommended Jayce and Elise. Despite arachnophobia, I did actually find Elise somewhat fun to play)
TL;DR:
is a strong generalist, and is probably worth trying at least.
Few champs are as versatile as
is a good mage with a strong early game. She can support herself better than she can support her allies though, but is still a good support with plenty utility.
is a great support and has damage even Lux would write home about, not to mention a lot of utility through her passive. Easy to play too! Short range and squishy though.
Hope you find it helpful, and I hope you like the mentioned champs if you chose to give them a shot.
GL&HF!