Regarding frequency first, 訪れる is roughly three times more common than 訪ねる on BCCWJ. 訪れる is seven times more common if we limit the results to Yahoo! blog/chiebukuro articles, which indicates 訪ねる is even less common in relatively casual written materials. I personally think you should master 訪れる first. But 訪ねる is not uncommon at all, and you may have to learn it before JLPT 1 level.
IMHO, ～を訪れる is a neutral word usable in business settings and other everyday situations. You can also say ～に訪れる. (Note that 訪ねる is not a keigo and you often have to use honorific いらっしゃる or humble 伺う/お邪魔する instead.)
On the other hand, when an object is a place name, I feel ～を訪ねる is a rather literary and somewhat "nostalgic" term typically used with historical attractions (石川啄木ゆかりの地を訪ねる), one's hometown (母校を訪ねる), temples/shrines (東北の神社を訪ねる旅), etc. Using it with nearby modern facilities (e.g. 駅前のクリニックを訪ねる) is fine in stiff novels, but it can sound a little off in ordinary blog articles and such.