We are based in Osaka for 4 nights Are you now in Japan?
In which area of Osaka City are you staying?
(Umeda, Namba, Shin-Osaka, or else?)
we plan to do day trips to Kyoto-Nara-Arashiyama-Gion and other areas within Kyoto and Osaka. Nara City is in Nara Prefecture, neither Kyoto nor Osaka.
Arashiyama and Gion are parts of Kyoto City in Kyoto Prefecture.
[Nara]
JR Yamatoji Rapid trains are available from morning to evening
for the section Osaka -- Nara (-- Kamo).
A one-way Rapid train ride between Osaka and Nara
takes about 50 minutes.
Trains departing at Track 1 of Osaka Station
run in five directions;
Yamatoji Rapid trains are bound for Nara or Kamo.
Major sightseeing spots in Nara City
are accessible from Nara Station on foot or by bus.
A Nara Kotsu 1-day bus pass for Nara Park and Nishinokyo
pays off for three or more bus rides inside the usage area.
http://www.narakotsu.co.jp/language/en/pass.html(When you plan to visit some sites
also in Ikaruga Town (e.g. Horyuji Temple)
or in Asuka Village (e.g. Takamatsuzuka Tomb),
it would be better to add one day.)
[Kyoto]
I recommend that first-time Kyoto visitors have at least two days to explore the city.
JR Special Rapid trains are available from morning to night,
which make stops at major stations
including Osaka, Shin-Osaka and Kyoto.
A one-way Special Rapid train ride
between Osaka / Shin-Osaka and Kyoto
takes about 30 minutes / 25 minutes.
Please pay attention to morning and evening commuters' rush on weekdays.
A Kyoto City Bus & Kyoto Bus One-day Pass
pays off for three or more bus rides inside the usage area.
https://www2.city.kyoto.lg.jp/kotsu/webguide/en/ticket/regular_1day_ca...(The road traffic may be congested during busy tourist seasons.)
While non-JR railway (including subway) and bus lines
are convenient for visiting many sightseeing spots in Kyoto City,
Arashiyama can be accessed also by JR Sagano Line.
A one-way Local train ride
between Kyoto and Saga-Arashiyama
takes about 15 minutes;
Rapid trains go a little faster.
Sagano Line trains depart at Tracks 31 to 33
near the Central Gate,
around the north end [Karasuma end] of Kyoto Station.
From Kyoto Station,
you can travel by (JR) Nara Line
to Inari Station (close to Fushimi Inari Taisha)
and to Uji Station (in Uji City, close to Byodoin).
Takao in Kyoto City is accessible by West JR Bus Takao-Keihoku Line,
which is covered by Japan Rail Pass.
- Gion
https://www.japan-guide.com/e/e3902.html- Arashiyama
https://www.japan-guide.com/e/e3912.html- Fushimi Inari Taisha
https://www.japan-guide.com/e/e3915.html- Byodoin
https://www.japan-guide.com/e/e3923.html- Takao
https://www.japan-guide.com/e/e3940.html