Erm. Idk if its worth to get the JR Pass for 7 days if you're only gonna use it for hakone. Cause its 33000yen + 5700yen for hakone pass. Not sure about your currency but when I convert, it's already $470.

If you just use the hakone pass, it includes the shinjuku round trip which takes about 1.5h to get there. Your trips around Tokyo shouldn't cost more than $100. Perhaps you can just get the earlier train and save the money? Haha.

For me, I'm going to Tokyo in July and was thinking of taking this tour https://www.kkday.com/en/product/20194?cid=4904&ud1=detail-share&ud2=app-android

(Of course, you will have less freedom to sightsee and the itinerary will change if there's bad weather)