As for why it is so close, Peking University is not Peking University, but yenching university. The earliest Peking University is in the city, which is quite far from Tsinghua.

Then why is Tsinghua next to yenching university? Probably because that place is a royal garden with three mountains and five gardens. Moreover, Haidian was desolate at that time, so it was natural for universities to choose these gardens as the basis for expansion.