When should I visit a prospective school?

Essentially, I have an LSAC GPA and LSAT above the 75th percentile for all T14 schools, and so I was thinking to visit my top choices, Harvard and Yale. I'm not sure when to visit though. I was thinking of visiting early September, to get it out of the way and to focus on my last year of school, but I wouldn't have submitted my application by then. Should I visit after submitting my application? Will it make a difference in terms of them knowing I was there etc? Thanks in advance for the help!