Osaka

Hi,

Since you are flying and not doing any long distance travel, no JR Pass is going to help you - although there are a few regional passes that might save you some money. For getting from KIX and into the city, plus local transport, you might look at getting the Icoca & Haruka discount ticket. It gives you some good savings on the Haruka train into the city, plus the Icoca card can be used in Osaka, Kyoto, and Tokyo. You can read more on using IC cards in Japan here. You can also add more money on to the card if it gets low.

You are definitely going to need to rearrange some of your plans though. The end/start of the year is a big holiday period in Japan. You mentioned going to the ramen museum (which I presume is the Cup Noodles Museum in Ikeda. But it will be closed Dec 26 - Jan 2. So that is out. In fact, nearly all museums will be closed, and most restaurants will be closed over New Year's as well. Fortunately the convenience stores will still be open, so you don't have to worry about finding something to eat. For the end/start of the year, to avoid being disappointed, I strongly urge you to check every single place you plan to go first - many places will be closed from around Dec 27 - Jan 3rd or 4th. Most temples and shrines will be open, but not all. You do have the opportunity however to experience the Japanese New Year. If you still have your heart set about seeing a ramen museum, then there is a more famous one in Yokohama, and it should be open right after New Year's.

In Osaka, seeing the Umeda Sky Bldg should not be a problem, and if you like, there is also the newer Abeno Harukas Bldg. The views from each are quite different.

USJ will be open til 9 PM, except New Year's Eve which is 7 PM.

I also highly recommend you take a half day to see Nara also. Missing the Todaiji Great Buddha would be a tragedy. Nara Park has a lot of other great places, such as Kasuga Grand Shrine, Kofukuji Temple, and feeding the many deer in the area. You are giving very little time for Kyoto, although you could spend 2 months there and not see it all.
For Kyoto, to make your time more efficient, you could go to places very early or late. The Fushimi Inari Shrine is one of Kyoto's Top 3, and it is open 24/7, so fitting it in early in the morning or evening allows you to add other places in between, plus you can avoid a lot of the crowds at either time. The Honganji Temples open at the crack of dawn and are within walking distance of Kyoto Stn. so they are easy to fit in too.

You didn't specify which airport in Tokyo you are using, but if Narita, the cheapest way in and out is the 1000 yen bus. In Tokyo, if you want to use a subway, you might consider a 2 or 3 day subway pass.
For going to Hakone, you can use a Hakone Free Pass to save money. The Loop Course is a common way to see all the sights and takes a full day.

Best of luck, and Happy New Year.