For example, how would I say something like "Harvard rejected me" or "Harvard accepted me"?
reject: 拒绝, 驳回, 否决, 否认
Harvard rejected me.
accept: 接受, 答应, 采纳, 采用, 接纳, 录取
Harvard accepted me.
Probably the OP is thinking of 錄取. This is the verb that means 'admit'; 'give a place in a class', 'allow to register as a full-time student.' It is perhaps more common (in China) to say something like 考進某大學, meaning you have passsed the admission exam or just 進某大學 'to enter or get into a university'
The opposite of 錄取 is simply 沒有錄取, there is no separate verb such as 'reject'. It is also of course possible that a school accepts/rejects your application for a job, or even accepts/rejects you or your ideas as good/smart/moral etc. These senses one would not use 錄取, but other words such as 聘請 or 雇用人 for jobs, or 接收人 for your moral probity or fellowship.