Transportations of Kinki Area and where to get discount passes.

Where to get discount tickets
https://www.tourist-information-center.jp/kansai/en/kix/information/#s08
Where to get Keihan discount ticket
https://www.keihan.co.jp/travel/en/tickets/special/kyoto-osaka

Transportations of KinkiArea
"arrangement of transportation of Kinki Area"
Osaka area is center of Kinki area, Kyoto is 30km north-east and then go to Nagoya and Tokyo. Nara is 20km east and over mountains to east, there are citys of Mie and then Ise Bay. Kobe is about 30km west and then more 40km to famous Himeji castle.

Then explain from Osaka area.

there is a circle line of JR(Japan railway) at outside of Osaka City. And  many Metro line runs vertically and horizontaly in the circle.
Vertical center line of the circle is M-line of Osaka metro. And "many terminal of JR and private railways" are on the center line. From top side Osaka-Station (Umeda station)(M16) which is also terminal of JR and Hankyu Railway(HK line to Kyoto and Kobe). Little bit down side of the center line, Yodoyabashi (M17) which is a terminal(KH0) of Keihan Railway(KH line to Kyoto). At the center of the line is Namba station which is a terminal of Nankai railway(NK line to Kansai Airport and runs more far to Wakayama city. From Wakayama city runs east to Koyasan). Also from Namba station Kintetsu railway(A line to Nara). Bottom of the line is Ten-noji (Abenobashi) which is terminal of JR and Kintetsu (E and F line)

From the bottom end (Ten-noji) of the Circle, JR runs south to Kansai Airport, and runs more to Wakayama city. Then, runs north to Kumano-Kodou(old route).

Next explain about Kyoto.
Kyoto basin located 30km north-east of Osaka. From Osaka station JR run to  Kyoto station and then through it to Nagoya and Tokyo. Hankyu railway from Osaka station go to west Kyoto named Arashiyama and then through Kyoto city to east side of Kyoto named Kawara-machi station which is near Gion-shijyou of Kaihan Railway.

Keihan Railway go from KH0/Osaka to Kyoto and run along east mountain range of Kyoto where most view points are there.

Kyoto metro are only 2 lines cross verticaly and holizontally. Therefore it's not so comvenient. So many bus lines are used for transpotation in the city area. There are so many tourist, so buses arevery crowded.

Nara is very old and interesting city with many deers, and very small city but not so much tourist compared with Kyoto. So easy to see around only city area. However Nara is famous about hiking in native forest and old rural area. It takes time more than see around city area tour.
Yoshino area rather far from Nara is so famous for cherry blossoms.

Kobe is very decent and fasshonable city, so I don't know well about the city. My wife know better.
If you are interrested about Kobe, I will reserch.

How you can come to my guest-house.
My guesthouse is located in Hirakata-koen (Koen means park) (KH20)and Keihan railway (KH line) run through the City. There is a big park named Hirakata-park in Hirakata-koen.

So at Kansai airport (KIX), you buy "Nankai-metro through ticket via Namba" which cost 1000yen, And take limitted express or express to Namba terminal then change to Namba/Osaka metro  station (M20) with same ticket to Yodoyabashi (M17), then buy ticket and change to Yodoyabashi/Keihan (KH0) and take express or sub express to Hirakata-koen(KH20) or take limitted expree to Hirakata city(H21) and 1 station back to Hirakata-koen(KH20). It cost 330yen. Therefore total is 1330yen / person

Transportation fee to Kyoto
You can use discount 1 day ticket for foreigner of Keihan named Osaka-Kyoto ticket cost 800yen. (2days ticket is 1,200yen). So when you see around East mountain range, you need only this ticket.

When you go to other place of Kyoto, better to use 1 day ticket of Kyoto City bus which cost 600yen.
But those do not include tickets for facility entrance fee.
Usualy each entrance fee costs about 500yen.

Transportation fee to Osaka
You can use Kyoto-Osaka and Osaka Metro day pass cost 1,400yen. You can use this for Keihan and Osaka metro and Osaka bus unlimitted ride.

Transportation fee to Nara
You can use also discount ticket named Nara and Ikaruga (old rural area) ticket cost 1,700yen.

You can see the detail of above tickets in the web searched by "keihan railway", and also you can see various view points in the web. Please try.
Also station name are searched by "Nankai railway", "Hankyu Railway","Osaka metro", "Kyoto city bus".
My guesthouse will be searched by "Hirakatapark guesthouse"

Kansai area train map
http://www.surutto.com/tickets/kansai_thru_english.html
Keihan railway
https://www.keihan.co.jp/travel/en/
Nankai railway
https://www.howto-osaka.com/en/top.html
Hankyu railway
http://www.hankyu.co.jp/global/en/
Osaka metro and bus
https://www.osakametro.co.jp/en/
Kyoto metro and bus
https://www2.city.kyoto.lg.jp/kotsu/webguide/en/index.html

 I will write here ordinaly transportation fee.
(you can check by Keihan railway web)
By Keihan railway, 
from osaka to kyoto is 410yen to 430yen.
from Osaka to Hirakata-kouen 330yen.
from kyoto to Hirakata-kouen about 350yen.
There is a prepaid refundable and chargeable IC card named ICOCA. the Card is usuful almost in all of Japan, but refundable only in Kinki area.
Where discount ticket can not be used,ICOCA card is very convenient.

Where to get discount tickets is as follow.
https://www.keihan.co.jp/travel/en/tickets/special/kyoto-osaka