You should be able to store your luggage, there should both be coin lockers as well as luggage storage service. I never had reason to use them though, so can't say anything for sure. There are definitely coin lockers at train stations in Tokyo, usually the bigger the station, the bigger coin lockers you can find.
I don't know about any tours, how confident are you to do it yourself?
If I were to recommend what to do to see some of Tokyo and have limited time, one option would be to take the Skyliner from Narita to Ueno (about 40 minutes), get out south, walk down Ameyoko towards Okachimachi on one side, then back to Ueno on the other side, then use Ginza Subway from Ueno to Asakusa (about 5 minutes) and go to the Buddhist temple there (Sensoji). It's a tourist spot, but if you don't mind that, it's still a nice and close by place to get some "Japan", with a lot of small souvenir shops. There is also the Keisei Narita Sky Epxress which is half the money compared to the Skyliner and goes from Narita to Asakusa in about an hour.
Alternatively and in my eyes a bit more interesting, get into JR Yamanote Subway at Ueno and head to Harajuku. Doesn't really matter which direction, as Yamanote goes around in a circle and Harajuku is more or less the furthest away (about 35 minutes). The train runs every couple of minutes, so if you "miss" one, don't worry. Just make sure to not miss your train back to the Airport, as the Skyliner does not run as often (about twice an hour).
There you can head south and west, towards Omotesando for rich people shopping stuff, or also west for Takesh.ita-dori (without the ".", but the word would get censored) for youth fashion stuff, east for the Meji shrine, and with good chance see part of a traditional Japanese wedding, or go south and around the corner east to enter Yoyogi-park, to see all sorts of stuff, though probably not "traditional" Japanese.
If you ride JR or Subway in Tokyo and don't don't know which ticket to buy, you can always go for the cheapest and do "fare adjustment" before you leave the station at your destination, same cost. Just make sure to get the right type of ticket, so either JR or Subway, or you might have trouble entering through the ticket gate. Sadly, they don't mix.
There are also Airport busses that go to certain places in Tokyo, which might be more convenient, though I've never taken any other than the bus that goes straight to Haneda Airport.
Other than that, there are probably tour busses going from Ueno-station or at least Tokyo-station, though I've never done any of those.
