Budget Vacation Help - Tokyo Metro + Hakone?

Question:

We are a family of four (2 adult children and our 60 yr.old parents) visiting Japan for the first time this coming Spring. We want to spend 2 weeks in the Tokyo metro area, but the Yunessun resort in Hakone sounds really nice. Everyone left the planning of this whole trip to me and I'm a bit overwhelmed! So, to take a bit of the load off me, can anyone suggest a plan regarding transportation? I know a rail pass is a waste if we're only gonna do Tokyo metro, but what about the day trip to Hakone?

I know we'll arrive at Narita airport and stay at the Park Hyatt Shinjuku. So, what's the cheapest way to get:

from Narita to the Hyatt
from the Hyatt to Yunessun for an entire day
from Yunessun when it closes back to the Hyatt
and, finally, from the Hyatt to Narita on the final day

plus, of course, the cheapest way to get around Tokyo metro for all those in-between days!
thanks in advance, everyone, for any help!

Answer:

http://www.odakyu.jp/english/freepass/yu… the site for Hakone Yunnesen and Odakyu rail transportation and its fare.
http://www.limousinebus.co.jp/en/bus_ser… is for Limo fare Narita/shinjuku.
http://en.wikipedia.org/wiki/Suica is for a versatile fare card to get around on surface trains, subways, buses.
http://www.hatobus.com/en/index.html is the site where I strongly recommned you to plan your days in Tokyo.

from Narita to the Hyatt,
I recommend you to take Limo bus service, because it's cheaper and easier to get your Hotel. 3000yen each in total 12000yen for your party while taxi cost about 22000yen.

from the Hyatt to Yunessun for an entire day
The best way to go Yussun is walk (about 10minutes) to Shinjuku stn and take Odakyu line as explained in the above web site.

from Yunessun when it closes back to the Hyatt
Take the reverse route of the above back.

and, finally, from the Hyatt to Narita on the final day
Take the Limo back to Narita.

the cheapest way to get around Tokyo metro for all those in-between days!
The cheapest and fruitful way to get around is to get "suica" with which you can ride any bus, trains(surface/underground) including Odakyu lines.

Additionally I recommend you to consider making good use of "Hato bus" for sightseeing of Tokyo.