Ori, Caitlyn, Udyr, Amumu, Jax, Pantheon, Nami, are pretty well balanced in my opinion.
Ori, Cait, Nami are strong champs, but all have counterplay. Nami requires landing a difficult to land skillshot and good positioning, Cait requires good kiting and positioning with a clear advantage (her range) and clear weaknesses (not incredibly mobile, not a great duelist, not that strong at all ins), Ori requires landing skillshots, smart use of skills, good positioning, good teamplay.
Udyr I think is balanced because he is a champion with very clear strengths (waveclear, jungle clear, tankiness, speed, dueling potential, counter jungling) and weaknesses (easily kited, mana reliant). Amumu, Jax, and Pantheon are similar. Amumu and Pantheon (jungle) suffer from poor early mana sustain. Amumu is very vulnerable to being killed in his jungle, while Pantheon is strong early and relies on applying enough early pressure to begin snowballing. Jax and Amumu both have weak early games that scale well, but both can be countered with proper cc chaining or disengage.