I've been struggling against the endless hoards of Master Yi's recently and I need to start playing a good champion to lock him down since my roster includes a fairly small amount of CC, most of which are slows which don't effect Yi.
Any suggestions for fun CC-heavy champions? preferably with a lower IP cost, but I'm flexible.
It really depends on what role you're looking at. Since you didn't mention I'll just toss out a few
Support: 
Jungle: 
(Can't emphasize Rammus enough, perfect counter to a Yi), 
Top: 
Mid: 
Tried to keep the list to cheaper champions and less mechanically intensive ones. All listed have a very reliable delivery source for stuns and function well against Yi.
easy to learn
has point & click root which also makes him untargetable so yi wont be able to use his q on you either and even if he Q's somebody else you will follow him anyway.
Has a spammable mini knockup to intrupt what he does
and can use ult to reduce his dps by 20% for all your teammates.
I reccomend maokai for different reasons aswell
Sapplings can be used for wards
because even if you suck with him point and clicking yi or any other carry wont be difficult
and even if you were a complete zombie eggplant you can still just stand near your allies with ult active and reduce all incoming damage by 20%
Lulu's Whimsy is one of the most amazing CCs in the game, in my opinion. Not to mention the fact that she also comes with a knockup that's ideal for disrupting enemies that try to engage at melee range.
you wanted targeted hard cc? 
are some of the best bets out there.
realistically you want ryze to seriously put the reigns on someone whos snowballing in order to cripple them/their team.
-the queen of CC. She's mainly a support but can go jungle (I've done it before, it's quite fun. Ganks are god tier).
-great CC with a knock up, heavy slows, and AOE stun. Damage is unreliable though.
You're welcome.
Actually, Yi's weakness is proactive champions that can force snowballs/objectives while Yi's still farming. It's extremely difficult to beat a Yi, especially a good one, at straight up fighting; the smart route is to instead step on all the areas he's most prone in. It's also a little difficult to suggest CC champs because they tend to be Tanks and Mages, the two classes I'd say Yi has the easiest time killing.
Skarner's a pretty big asshole towards Yi if you're looking at it from a CC perspective at least, while also holding huge neutral objective control. Jax on the other hand is one that can go toe to toe with Yi if you can maximize the amount of progress you can make within the same time frame as Yi works in.
Lissandra?
I always pick to stop the Yi.
Poly-these-nuts
Oh also I feel very fucking useless when I play her other than suppressing the Yi. N3rf$
I'd recommend Sion, but that's not reliable.
Naut and Maokai have the most reliable CC for tanks.
Worry not, wait for a week (patch 6.9/ jungle changes) and then he'll be pushed out of tank/bruiser forms.
Early Game ( Yi with just sabre) in jg - 
if played well. ( no one has 0 CD CC abilities). Actively counter jg his RED+Rift Scuttlers,
Mid Game ( Yi with one damage item) - 
etc. They have burst damage/CC to poke/burst from range.
Late game (where Yi everyone has items) - **TEAM **effort ( 
, 
IDK if these were mentioned.
the most reliable cc ability is maokai twisted advance. because there is no way to escape it.
targeted fear, and since Yi's ult makes him immune to slows, he just ends up running away super fast. I think there's no travel time either, so as long as you can cast it on Yi, it will hit him, so he can't alpha strike away from it.
is also really good if you don't want Yi running away from you, lol.
Nautilus is fun. And if you can pick up a RoA, you pretty much one shot squishies with your ult
depends, you want a tank? fighter? mage? adc? jungler ? support?
Thanks so much everyone.
I realized that I actually own Maokai but I've only played him lke twice. I'll start practising and hopefully take him into ranked soon.
Maokai. Targeted snare, all you could need.
Watch him run to the other side of the map.
Lissandra has her frost nova and a targeted stun Alistar and Janna are the king and queen of peel Varus, Ashe, Vayne, and Tristana all have pretty reliable ways of stopping someone who is in their face
