I will be doing an unpaid internship in Japan for a little under 90 days with just the tourist visa, but I also wanted to go with my friends before the internship for a couple weeks to sight see but that will take me over 90 days. Is it possible to do the sight seeing with my friends, then go to Korea for a few days, then come back for my internship to reset the 90 days? If not is there any other options? I was thinking it may be okay if I bring proof that I will leave Japan like a flight home, but will they ask for a returning flight when I enter the country? I am a United States Citizen.
Yes, that should be fine. Your first trip to Japan is as a tourist, which is OK, and your second trip is as an unpaid intern staying under 90 days, which is also OK. Source: http://www.moj.go.jp/nyuukokukanri/kouhou/nyuukokukanri07_00109.html
You may be asked for a return ticket when checking in or when entering, but showing a ticket to Korea is fine for this, since they only care that you leave Japan, not that you return to the US.
Also, while doing the same trips in reverse (3 mo internship first, tourism later) is also technically OK, it's going to raise a lot more questions since that would look an awful lot like the "visa runs" of people illegally working in Japan.