Yeah, the private lines in Kansai have a week long unlimited use pass or something that's cheap. Personally, since the changes in Harajuku went through in Tokyo I've actually been recommending as Osaka/Nara/Kyoto only trip to anyone who asks about Japan. There's tonnes to do there and the food is cheaper and better so good pick!
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In Osaka: In addition to Doutonbori be sure to check out the old town near the base of the tower (next to Spa World: Japan's probably only stay-over type jjimjilbang, and amazing in itself). Very cheap eats and all old-skool postwar reconstruction Japanese. If you go to the castle park, there's an old guy who hangs around the castle exterior practising his English on tourists by telling them about the place for nothing. He's an absolute champ so grab him a beer or something if he shows you around. Osaka also has Japan's only museum that talks about wartime atrocities. Haven't gone myself but I heard it's interesting for history buffs. A walk through New Hida could be something like none other (see section 12 here http://www.hellodamage.com/top/2010/12/05/shinya-kusakas-ura-hello-work/
) See a Don Quihote (Donki's) variety store. They're in every Japanese city but going inside is an utter trip.
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In Nara: Almost all the attractions are located in one giant park so its easy to see it all and it is amazing
. The main temple is a spam-fest of stone lanterns. Don't skip a walk through the primeval forest (theres even a little boobshrine there if you pay attention). The deer are jackarses. The rest of Nara is concrete garbage.
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In Kyoto: Inari shrine is a must see. Absolute gate-spam. I got lost there at night once. Kiyamizudera is famous for good reason too. Stroll Gion at night. That's the south end of town: use public transport there. On the north side, the Golden Pavillion and Ryoanji are mostly letdowns due to being nothing more than a tourist trail with designated photo spots and souvenier spruikers bugging you but take your obligatory "been there" photo. The rest of the north end of town near those two however is great. Hire a bike.
The train station here still lacks an adequate map, but at least its 10x easier to get to the English tourism info booth than when James May had a fit about it on TV.
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Personal recommendation for a daytrip that's off the beaten path? Mt. Koya
. End of some private line that runs from Osaka Namba station. It links up with a cablecar and bus and... don't worry, you get herded between them like cattle. Easy daytrip.
It's basically a township nestled in a thin shallow mountaintop valley south of Osaka. The west side of town is only atypically shaped temples, the east side is one humongous ancient cemetary: in summer it gets all misty and mossy and atmospheric with vines and creepers tangled around partially collapsed crypts. Astoundingly pretty. The new quarter is probably the most bizarre cemetery you'll ever see. A flyspray company has a shrine there apologising to all the bugs it has indirectly massacred.
The entire township and the hiking trail up there is UNESCO World Heritage but it doesn't see many Western visitors. Most of the tourists there are Japanese arriving doing final preparations for the 88 pilgrimage before hopping on a tourbus to Shikoku. You can do templestay there if you book ahead but it'll cost you approximately two of your firstborn's kidneys. One main draw for the stays is the amazingly tasty vegetarian temple food so I've heard which is great because there is in fact a restaurant smack bang in the centre of the town (south side of the street near the crossroads) that sells it to anyone for far cheaper XD. Forget every bland thing you've thought about vego cuisine.
There's actually another boobshrine here too, but it's tucked away at the start of the hiking trail.
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Other places are Iga-Ueno, the "ninja village" (the historic ninja house attraction is good, but the rest is progressively having the historic bits replaced with homages to "Naruto"), just south of Nara. Laugh at the Western tourists buying their kids "replica ninja shoes" for insane prices when the real deal are still made in the Philippines for a buck and sold downtown for eight. Its traditional rival village is also nearby so you could poke your head in there instead and see if its less touristy.
East of Iga-Ueno, and getting farther afield, so check a map, Yoro has a park that attempts to make you injure yourself which is ... memorable. Ise is the most sacred place to the Japanese, but probably a bit too far.
Somewhere east of Kyoto there's Japan's second most famous penisshrines.
West of Osaka, don't overlook Kobe. The Mt Rokko nightview is deemed the 2nd or 3rd best in Japan.
Further West of Kobe again, Himeji of course has one of Japan's few remaining original (non-reconstructed) castles.
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Say a little about yourself and your interests and I might be able to make further suggestions along those lines, hey. I've travelled around that area a fair whack so feel free to contact me via PM.