Yi and Trynd are quite easy, but they're AD champs. They're low strentgh early on, but late game all they need to do is right click once and then maybe use an ability or two to win. Mages aren't easy in the same way, since all need to use abilities. I'd say the easiest mages are the ones who can both deal high damage, and escape easily, such as LeBlanc and Ahri. LeBlanc is probably one of the easiest mages, you can have up to 2 blinks, up to 2 silences, and up to 2 slows/snares. That is some super easy escaping, especially when combined with flash. Ahri has Charm and 3 fucking blinks, it isn't a challenge to escape as her either.
The ones with no real escapes are actually harder to play I'd say, if your Flash is down. Sure Veigar can just spam his skills, but he actually works like an AD carry: He needs farm. It isn't gold farm, but AP farming with his Q, so when the other mages can gank and get their wealth off of kills, Veigar needs to sit in lane and last hit with Q all the time, always when he can. Good Veigar has near 100 AP at 20:00 min from that only, which can help a lot. If Philosopher's Stones could still be stacked, I'd say 3 of them would actually make Veigar super good if let to farm with no resistance.
Annie is easy to play too, though, because all of her abilities can stun. Veigar needs to rely on a long cooldown stun which can be escaped if you have a blink, all Annie needs to do is BAM TIBBERS IN YO FACE and if the chaser is low enough, maybe cast the two other spells.
This is also why someone such as Karthus can be extremely hard to play even though "he can just press R". Those Lay Wastes need aim, and if you can't do that, you do awful. Karthus is actually a ranged carry, he just doesn't stack AD like others do, and he doesn't just right click on the target like they normally do. Karthus has to fucking aim all of his shots, make sure Lay waste hits either only one enemy, or all the possible enemies at the same time.