Recommended Japanese Universities?

Hello, I was considering going to a university in Japan as I just love the country and its history. However when it comes to a higher education I am not really sure where to start, I highly doubt I could get into top tier universities such as University of Tokyo and others like it. I've looked into other universities and I've heard some mixed reviews about Temple University and that Sophia University, while an okay school, is really expensive.

Any recommendations for a person who can speak beginner level Japanese?

P.S Just a side question, but if I applied how would universities abroad look at online classes, would it negatively or positively influence their choice? Or would it matter if I just got good grades in it?

Thanks in advance.