Having been a junior banker myself (and with friends at most banks across wall street) I can tell you that virtually no one is being taken to events or spending days socializing as an intern, let alone as an analyst or associate. You spend your days preparing pitchbooks (to pitch companies on why you should be the bank representing them), building financial models and putting together management presentations (in addition to any one-off requests your senior people or the client have). Can go into more detail but it's covered pretty well in comments above.

(Also there's no such thing as shadowing a manager in investment banking - just doesn't exist. There are mentorship programs that the banks run, but the vast majority of the time they consist of getting coffee at most once a month)