Hi there,
Arriving late at Kansai Airport, you can stay the night at the airport, sleep on one of the benches or spend the night in the Internet Lounge. There are also a range of Hotels available around Kansai Airport, including budget hotels. Which may be a better solution, given that you just had a flight and want to be fresh for a full week of exploring Japan. You can also still make it to Osaka if you arrive around 10 and book a hotel there that allows for late check-in.
It will beneficial to get a 7 Day JR Pass for sure, judging from your planned itinerary. The Shinkansen return between Tokyo - Osaka/Kyoto is about the same price, so all the travel after that is what you save :)
Here is a little list to illustrate what I mean:
Kansai Airport --> Shin-Osaka by Haruka express ¥ 2,770 (assuming you stay the first night at or around the Airport).
Shin-Osaka --> Tokyo ¥ 13,750
Tokyo --> Osaka ¥ 13,750
Osaka --> Kyoto ¥ 540
Kyoto --> Kansai Airport ¥ 3,280
This adds up to ¥ 34,090 The 7-Day JR Pass is 28,300, so you would save ¥ 5,790. This is not including any rides you will make on the local JR lines within Tokyo and Osaka, which will certainly make for even better savings.
The Pass will get you to the bigger share of the places you want to go but some will require a different kind of transport. In Tokyo this is only Odaiba. But you may as well make the best of it and ride the Yurakamome there, which is a mono rail like train without a driver! Personally I think its really cool!
The Skytree may be a little bit confusing to access by JR too, you can ride the JR Sobu line from Tokyo to Kinshicho and walk from there (its about 30 minutes, but you can't get lost, because you will always be able to see the tower).
Other ways of reaching the Sky Tree can be found here on the access page.
For Kyoto, I would recommend buying a one day bus pass which is just ¥ 500 and allows you to travel to all of the sights you plan to see!
Hope this helps,
Daniel