Third Day:  After bread fast headed to Shin Osaka Station. There was slight drizzle and the weather was cold, I supposed it should be around 12 degrees.  We proceeded to our first destination- Osaka Castle by taking Midosuji Lie to Hommachi and transferred to Chuo Line and got off at Tanimaci 4-chome Station. Umbrellas/wing breaker  became handy because it was still drizzling. We walked all the way to Osaka Park and the drizzle finally stopped. Osaka Park is definitely very huge so we just covered a small portion of it and proceeded to buy ticket to visit Osaka Castle. Spent the whole morning  there. 
We walked back to Tanimai 4-chome station and to take the Chuo Line to Hommachi Station. Our initial plan is to walk from Hommachi to Shinsaibashi  but the sky started to get cloudy and rain began to fall. So as an alternative we took the Midosuji Line and got off at the next stop e.g Shinsaibashi Station. We spent the whole afternoon in Shinsaibashi and Dotonbori area because the rain was getting heavier.  Shopping and eating okonomic, octopus balls, ice cream and many more which I got confused with their names.
Head back to hotel by taking Subway Midosuji Line.
Our visit to Osaka was indeed very brief, so much so that we had missed out many tourist spots like Arashiyama and Kinkakuji .
But Japan has given us such a good and deep impression that we will return very soon if not Osaka again then may be Hokaiddo/Sapporo.

depend on where u going from n which pass u have.
i think 4 days Nikko pass is the best ( http://www.tobu.co.jp/foreign/en/pass/all.html ). it cover unlimited bus ride to Kegon/Ryuzu fall n the train from Asakura (i think) are slightly slower than JR's bullet train. (i took JR coz my JR passes still valid but it doesnt cover the bus to Chuzenji Lake area)

y Tobu 4 day nikko pass , coz bus to from Nikko station to Ryuzu fall coz more than 1k yen (pertrip). Kegon arent tat expensive. Kegon Fall is on walking distant from Chuzenji Onsen bus station. google for kanmangafuchi abyss nearby station. i was fusfrated with the jam (went there on weekend), i drop off early n manage to go faster than the bus pace.

if u worry, just head to Tokyo tourist centre n grab a brochure for it. it tell u time table n price for it.