Nagoya-Kyoto-Osaka-Tokyo-Nagoya

HI!
I am badly needing your help.
I will travel with two of my friends this coming July with the routes indicated above. We only have 4 days for all the places, now my questions are:
1. Is that possible? to visit these places in just 4 days? It is okay to us if we take night trip in trains.
2. Going to these places, what train and bus access should we take? I heard there is a JR pass do you recommend any?
3. Do you have any suggestions on the destination that we should prioritize?

Thanks a lot!

I assume you are flying in and out of Nagoya?
For 4 days, that is impossible, or waste of time. You will have barely any time to "see" any place in those cities. You would want 2 - 3 days just to see Kyoto, for example.

If you are flying in/out of Nagoya, I would at most spend half a day in Nagoya (for visiting Nagoya castle and Atsuta Shrine, if you are interested), then proceed to Kyoto and stay there. If you "must" go to Osaka for shopping or whatsoever, you could visit as a day trip. I would definitely skip Tokyo for that short a trip.

For the above cities, a 7 day JR Pass is recommended. That said, doing 4 cities in 4 days is near impossible. If it was some town or village that might be possible.

That said, if you are going in the peak of summer and you have full days (as in you won't be spending time trying to get off or the board the plane) doing all four cities in 4 days is actually possible, though you would barely be seeing any of each.

I recommend 3 options, only the thurd requires a JR Pass
1. One day in Nagoya for sightseeing
Two days in Tokyo for sightseeing and shopping
One day (or night ) in Hakone for sightseeing and to stay in a Japanese Ryokan

2. Spend all your time in one city
E.g. Tokyo, Nagoya, Kyoto
I would opt for Kyoto with your nights in Osaka due to Kyoto's dinners being more expensive than her lunches
Also, walking about Osaka river at night is charming
Though spending an evening along Uji River or Gion or Arashiyama in Kyoto is good too

3. Be the crazy dude you are
Day 1
From Nagoya, go to Kyoto
See Eastern Kyoto
Walk from Kiyomizudera past Yasaka Shrine, Heian Shrine, past Nanzenji, through Philosopher's path till you reach Silver Pavillion. Taxi to lower Kamo Shrine near Demachiyanagi.
Walk south along the river till you reach Gion. Hopefully see some Geishas and have some authentic though pricey Japanese cuisine.
After dinner, take the subway south to Fushimi Inari Station
See Fushimi Ianri at night

Day 2
In the morning go to see Golden Pavillion by train or bus.
Then to Ryoanji by bus or walking.
Then either take the tram or taxi to Arashiyama.
At Arashiyama, see Togetsukyo bridge over the water then go for lunch. Either go to one of the restaurants doing a Toufu set lunch meal or having a fanciful vegetarian cuisine at the restaurant in Tenryuji Temple's garden.
Either way, Tenryuji Garden is a must see location. After exiting the garden, you will see a bamboo grove. Spend some time either taking the romantic train or going up the hill to have matcha at an old villa.

Eitherway, take the JR line to Kyoto station before 6pm.
Take the train to Osaka. Then to Namba station.
Go and see Domtombori river area. Snack heavily. Have good food.

If you can get a night train from Osaka to Tokyo, good for you. Go reserve this train as soon as you get your JR Pass. If not, take a shinkansen or a night bus to Tokyo.
Benefit of Shinkansen. JR Pass makes it free
Benefit of night bus. Can sleep on bus.

Day 3
Tokyo sights
Meiji Shrine
Harajuku
Asakusa
Night out at one of the districts like Ginza, Shinjuku, Shibuya

Day 4
I don't get Tokyo. Maybe someone else can help you here
Go to Nagoya
Gake at Mt Fuji as the shinkansen zooms pass
See Nagoya castle
See Atsumi Shrine
See Aichi Science museum
5 hours for Nagoya is enough!

Thank you AK and Kanazawa! Very helpful. I have to talk to my friends and convince them to focus on atleast 2-3 cities. maybe I'll visit tokyo next time.
Other than Kyoto and Osaka, is there any other underrated places to visit near the area?