Cheaper way to travel in Japan?

My friends and I will be staying in Tokyo for a week and we will be coming from Narita airport. Since the suica+NEX package is no longer available, are there other promos we can avail of? Also people recommended the Jr pass, but I looked at the price and it doesn't seem economical unless we travel outside Tokyo, which we aren't. Are there other train promos? Thanks a lot!

NEX Tokyo Direct Ticket:
http://www.japan-guide.com/e/e2359_nex.html

Other options for travel between Tokyo and Narita Airport:
http://www.japan-guide.com/e/e2027.html

A list of Tokyo day passes is on the following page (scroll down about halfway):
http://www.japan-guide.com/e/e2017.html

Day passes may not save you money, however. If you are the sort who enjoys detailed planning, or someone who gets pleasure out of maximizing "unlimited rides" types of deals, you might be able to arrange your sightseeing to make use of one or more of these passes, but the savings are not likely to be more than a few hundred yen in a day.

You can look up fares on hyperdia.com to see if a day pass will save you money in support of a specific day's travel around Tokyo. Hyperdia is a little quirky, so it is recommended that you read the instructions on Japan Guide. (The examples are geared toward long-distance travel, which doesn't apply to you, but hyperdia is also useful for looking up routes inside Tokyo.)
http://www.japan-guide.com/e/e2323.html

There are some other deals available if you plan to venture a bit outside of Tokyo (for example, a day trip to Nikko or Kamakura or Yokohama). In that case, look at the Access portions of the Japan Guide pages for those destinations, or ask specific questions on this forum.

If you like museums, a good deal is the Grutto Pass that comes with two one-day Metro open tickets. (Scroll down to Metro and Grutt Pass 2014 on the following page.) Note that there are a number of interesting places covered by the Grutt Pass that are not museums, including some botanical and zoological facilities. (If you are planning to buy this package, just be aware that the day pass covers Tokyo Metro lines only, and not Toei lines.)
http://www.tokyometro.jp/en/ticket/value/other/index.html

Thank you very much to the both of you! Actually, we already made a day-to-day itinerary, but as I am not familiar with Japan, I don't know if we will be using the JR lines (because in the link you gave, most of the day passes do not include the JR line correct?) If you would kindly help me evaluate whether the day passes would be cheaper, I would be very grateful! The FF is our general itinerary:

Day 1 - Airport to Warabi Station (Warabi station is the station closest to where we are staying, so it is assumed that we will always go there at the beginning and end of the day)
Day 2 - Ueno + Asakusa
Day 3 - Hamamatsucho + Mitaka + Nakano
Day 4 - Mt Takao
Day 5 - Ikebukuro
Day 6 - Odaiba
Day 7 - Shinjuku + Kawasaki
Day 8 - Shibuya + Harajuku
Day 9 - Back to Airport

JR pass offers unlimited train rides on most JR trains within the pass's valid period (7, 14 or 21 consecutive days). You can ride most Shinkansen trains with JR pass. A JR pass will never pay you off without taking high speed bullet train. If your trip is just within Tokyo, JR pass is not for you.

http://whenshetravelstheworld.blogspot.sg/2014/04/japan-rail-pass-jr-p...