NRT is quite some distance from the city of Tokyo.
Different railway companies and some bus / coach companies offer services.
Buses take longer, trains vary from commuter-style to more modern cars. (URL at the end of this reply)
Tokyo has many "centers" and touristic sights are to be found all across the mega-city.
For neighborhoods to stay in you will get as many recommendations as you people.
Keep in mind that public transport in Tokyo is efficient but during peak hours trains are more than full (especially on section of the Yamanote ring railway line).
Here is my view as a long distance traveller:
If you are flying into and out of NRT
, and have no preference to stay in any specific neighborhood, I would select a neighborhood & hotel that allows easy transfer to NRT
For the March 2011 TYO A.net Meeting that was canceled last minute due to the Tohoku Earthquake and the resulting Tsunamis, I had opted to stay in the neighborhood of Inaricho, northeast of the very city center (if you take the royal palace as center of the city). Access to NRT
then can be to / from Ueno station (actually Keisei Ueno station).
The Keisei Skyliner surely is not the cheapest of options but is said to be fast and comfortable.
For hotels I had chosen Chisun Ueno, as it had been offering acceptable rates for a room that is larger than a shoe box. Always look at the square meter (or sqft) statement when reserving a hotel room in Tokyo !
As I have a preference to use public transport on rails over using buses in foreign cities, the train stations at Ueno as well as the Metro stations Ueno and Inaricho would give options for getting around.
Much more valuable information for getting around etc. can be found on japan-guide.com. Transport between NRT and Tokyo
Carpe diem ! Life is too short to waste your time ! Keep in mind, that today is the first day of the rest of your life !