7 days in Japan during Vernal Equiniox day

Is this itinerary doable especially that I may run into 2 days when attractions might be closed during Monday and Vernal Equinox day?

March/15: Arrive to Narita around 4:30PM take bus straight to a hotel in Tokyo
March/16: Tokyo sightseeing full day
March/17: Tokyo sightseeing full day
March/18: Take 6AM train to Kyoto, half day Kyoto
March/19: Full day in Kyoto
March/20 (Monday): Travel to Hakone to a Ryokan Onsen
March/21 (Tuesday): Leave early morning and catch my flight leaving at 7PM from Narita

Would it make sense to get the JR pass for this itinerary?
Would it make sense to take a train straight to Kyoto and then work my way back to Hakone and then to Tokyo?
I wanted to book the Ryokan for March/20 because the holiday closures.

Is this itinerary doable especially that I may run into 2 days when attractions might be closed during Monday and Vernal Equinox day?

Shops/Attractions don't close on Vernal Equinox day, on the contrary they will probably be busier on those days though.

Would it make sense to get the JR pass for this itinerary?

Yes. You could also use the JR Pass to catch the NEX (Narita Express) train to Tokyo/Shinjuku/wherever your hotel is in Tokyo. This will save you the cost o fthe bus ride (3000+ yen). You can also use it to get back to the airport.

Would it make sense to take a train straight to Kyoto and then work my way back to Hakone and then to Tokyo?

Yes, just take note of the best way to access Hakone from both Kyoto and Tokyo on the following page (using the dropdown box):-
http://www.japan-guide.com/e/e5206.html

I'd also recommend you purchase the Hakone Free Pass for getting around Hakone.
http://www.japan-guide.com/e/e2358_008.html
Purchase it at Mishima.

I wanted to book the Ryokan for March/20 because the holiday closures

Looks good to me, as mentioned no real closures though.

It is a pity that you won't be there a week or two later for the Cherry Blossoms. You might see a few early ones if you are lucky but in general I think you'll be too early.

Enjoy your trip!

Is this itinerary doable especially that I may run into 2 days when attractions might be closed during Monday and Vernal Equinox day?

Shops will not be closed because of the holiday, but smaller shops do tend to be closed one day a week. Whether that is Monday or some other day depends on the store. Attractions will be open on the holiday, but many will close the day after instead. That shouldn't be a problem since it is your travel day.

Btw, are you sure you have your dates right? March 20, 2012 falls on a Tuesday.

Thanks for catching that! So knowing that March/20 is national holiday and that Monday things might be closed.
Which way would it make sense to do this?
Tokyo-Hakone-Kyoto or Kyoto-Hakone-Tokyo
My only full day in Kyoto is Monday so that makes me nervous as I don't want to find places closed.

March/15: Arrive to Narita around 4:30PM take bus straight to a hotel in Tokyo
March/16: Tokyo sightseeing full day
March/17: Tokyo sightseeing full day
March/18: Take 6AM train to Kyoto, half day Kyoto
March/19: (Monday) Full day in Kyoto
March/20 (Tuesday): Travel to Hakone to a Ryokan Onsen
March/21 (Wednesday): Leave early morning and catch my flight leaving at 7PM from Narita

So knowing that March/20 is national holiday and that Monday things might be closed.

No, on the day following the national holiday, i.e. Wednesday March 21 some things might be closed.

I would try to avoid Hakone on a weekend and national holiday to reduce the crowds there.