Help with 5-day itinerary (Tokyo-Nagoya-Kyoto-Nara)

Hi,

I would like to know if the JR Pass is suitable and worthy for this kind of itinerary?
I'll be listing all the possible destinations we want to visit for our 5-day tour of Japan.
We'll be arriving first week of February 2016, is the winter climate duing this time really cold or can we still stroll outside?

Day 1 - Arrival at Kansai Airport by 8PM (We'll probably spend our night at the airport, is that possible?)
Day 2 - Travel to Shin-Osaka to catch the bullet train bound for Tokyo
- Tokyo tour: Akihabara, Imperial Palace, Tokyo Metropolitan Building, Shibuya, Tokyo Tower, Roponngi, etc.) Day 3 - Sanrio Puroland
- Catch the bullet train to Nagoya - Nagoya Castle - Bullet train to Kyoto Day 4 - Kyoto tour: visit temples and shrines in downtown Kyoto (possibly by walking: Golden Pavilion, Silver Temple, etc.) and Inari Shrine
Day 5 - Nara tour
- Travel back to Kansai Airport for the 9PM flight

Is this itinerary doable and will JR pass be useful?
Kindly suggest other options if you have something in mind that could help us minimize our expenses. We are budget travellers.
Thanks!

Regards,
Kaye