You can get a good free Tokyo tourist map from the tourist office in NRT.
The train map (with station names in English) is very easy to use, because all stations have numbers, so it is easy to see how long the distance is even if the line on the map is curved and difficult to follow. All signs and announcements on the subway are duplicated in English. There are two subway systems (Tokyo Metro and Toei), you can buy a daypass valid on both. The ticketing machines have a button to switch to English. Also there is a circular railway line called Yamanote Line, you need a separate ticket for that (sorry I don't know the details as I have only used it with a rail pass). For details on using the subway, I would suggest
www.japan-guide.com. In fact navigating the subway is easier than navigating when walking the streets (but many streets have English signs too).
The area around Tokyo Station is easy to navigate, so that if you stay there, you should have no problems finding your way back to the station (and if everything fails, catch a taxi and say "Tokyo Station"). If your budget is tight, you may want to stay near the Ueno station instead - the hotels are cheaper there and it is still relatively easy to navigate. Tokyo Station is walking distance to the Imperial Palace, and the Ginza shopping street. Ueno is close to Ueno Park with some museums and the zoo.
If you are afraid of getting lost, just take a GPS with you. I had one on my first trip to Japan, and while I never had to use it, it was comforting to know I could. Also use Google Street view before departing to get familiar with the areas.
Neighborhoods around either Tokyo Station or Ueno are not that exciting to spend a whole day there, so I would definitely take the subway somewhere else, for example:
* Go to the imperial palace (you will only see the fortifications surrounding the palace grounds, not the palace itself). Visit the palace gardens.
* Take the Hanzomon line to the Omotesando station, walk along the Omotesando boulevard to the Harajuku station and visit the Meiji shrine located there. It is nearly impossible to get lost there.
* Go to Shibuya to see the crowds of young hip Japanese people. The plaza at Shibuya station looks a little like Times Square with the giant screens, only nicer.
* Go to Asakusa to see the temple there
* Go to Tsukiji for sushi, you can also visit the nearby Hamarikyu Gardens.
Avoid going to Shinjuku, as it is easy to get lost there. Make sure you have enough cash with you, as ATMs accepting foreign credit cards are rare and don't work round the clock. Keep in mind that all public transport stops around midnight and taxis are expensive (every subway station has a timetable posted where you can see the last trains).