JR pass/ tokyo/ kyoto

So I was reading the conditions to the JR pass and I cant quite graspe the NOZOMI concept.

I am going from the narita airport to KYOTO. which to my understanding is the sanyo line/ tokaido line and then it says something about NOZOMI in which the JR Pass doesnt cover. My question is

What is the NOZOMI? is there more then one train for the Sanyo/ Tokaido line that isnt NOZOMI that I would be able to use the JR pass?

Another question is i will be staying several days in tokyo as well,
and was wondering if the JR line takes you all around and if the pass would work there.

I should be staying near the Chidori - Cho station and I want to visit Roppongi, Harajuku, Aikihabara, Asakusa

so that is why I am asking if it is wise and less expensive to buy the JR PASS?

The nozomi trains and the other train categories along the Tokaido/Sanyo Shinkansen are explained here:
http://www.japan-guide.com/e/e2018.html

Yes there are Hikari and Kodama trains you can take from Tokyo to Kyoto. Nozomi is faster, it just stops a few times. Kodama stops at every station and Hikari is something in between Kodama and Nozomi.

The JR pass is great to get around Tokyo. But I have heard that it's cheaper to buy tickets there if you don't need the JR pass for long travels. We've had 14 days JRpass both times so we've been covered during our time in Tokyo aswell. The JR trains goes all over the city so you should be able to go to all the places you want to see.

NOZOMI = Express Shinkansen
HIKARI = Rapid Shinkansen
KODAMA = Local Shinkansen

types of train
http://www.japan-guide.com/e/e2016.html

Google JR Yamanote line for JR transportation in Tokyo (this is not the only one but is practical). You MUST also read A-Z at the very top of each page on this site , especially the sections on transportation-trains. Most of your questions are answered there.

The Shinkansen Bullet train is broken down in to 3 kinds of trains. As mentioned above the the Nozomi and Hikari are express trains while the Kodama stops at every station. The Nozomi is a little faster than the Hikari but not by much. For most travelers the Hikari is fast enough. I lived in Japan for 14 years and only took the Nozomi 1 time and that was because my company purchased the ticket for me.

JR also has a whole set of different trains and the above is only talking about the Shinkansen trains.