Elizabeth said:
Arrived is "tuita." The second one translates "I left for the east exit."
This isn't exactly correct. "Arrived" isn't ideal either, but it does accurately reflect the fact that if you say 「東口に出た」, you're _already_ at the east exit.
More literally, 「東口に出た」 means something like "I came out (went out)
into the east exit." Remember that the 東口/西口/北口/南口 of a station doesn't just refer to the actual exit doorway itself but can also include the general area outside that you'll find yourself in if you leave through that exit. That's why you'll often see stores or restaurants or the like that describe their location as, for example 新宿駅南口 -- in this case, there's a good chance that they're located just outside the station in the immediate vicinity of the 南口.
At any rate, in this case, both "X ni deta" and "X ni tsuita" are describing someone who's already at the location. The difference is that the latter is focusing on the act of arrival, while the former puts the focus on the fact that you've come/gone out of, or 'exited' somewhere (i.e. the station) to get to an open area.
(I'd just also like to say for the record here that 新宿駅, with its 南口 and its 新南口, confuses me to no end every time I go there. That place is like kryptonite to my normally decent sense of direction.)