Hi there,
Welcome to the Forum!
Looking at the places you will visit, I don't think it matters that much where you go first. Personally I would go to Tokyo first and then go to Osaka, simply because you can do some shopping in Osaka without having to carry it with you all the time.
I have made a little itinerary what your travel in Japan could look like.
Day 1. Arrive in Osaka, If you have a long flight I would recommend staying here for a night to explore the city a bit and regain some energy.
Day 2. Travel to Tokyo and stay here for 3 Nights
Day 3. Tokyo
Day 4. Tokyo
Day 5. Travel to Osaka and visit Universal City.
Day 6. Day trip to Kyoto and possible Kobe as well.
Day 7. 10.30 am Flight back home.
Alternatively if you don't have to recover from any Jet Lag you could head on to Tokyo on the first day and Travel to Osaka on day 4 so you would have a separate day to visit Kobe or see more of Osaka it self.
A JR Pass is very well suited for this journey as the price is roughly the same as the Osaka - Tokyo and with all the extra traveling, you will be sure to make some nice savings! When you arrive at Kansai Airport you can exchange your pass there and use it for all the traveling that you will be doing by train!
It is quite hard to give a Hotel recommendation, I would recommend visiting a booking site such as TripAdvisor or Expedia.com and search for your own preferences and budget. Then you can read other customer reviews and be sure to book something nice!
Fortuitously I was looking at Spa Hotels myself yesterday and Royal Spa Hotel in Kyoto looked very promising, however I can't give a personal recommendation about it since I have not been there (yet).
Hope this helps you on your way.
-Daniel