For transport, like mentioned, just buy and load up a Suica card. Can buy them from a machine at stations. It will work on Subway, Trains, Buses etc. You tap into and out of the system, and it just charges you accordingly. We'd spend maybe $10 between two people per day using the subway a fair bit.
The subway system is amazing. I'm from Adelaide, Australia so it doesn't take much to impress me with public transport though. There are about 12 lines, and with a Tokyo Subway app, or just google, it's really easy to get around.
Rail pass is worth it if you're going to head down to Kyoto and around a bit. We planned it so we only needed the 7 day pass for our trip down to Kyoto, Nara, Hiroshima, Miyajima and back.
Some of these mentioned already, but some of the things we did:
Shinjuku (we stayed nearby) has great eating, nightlife, shopping. Shibuya has the famous busiest pedestrian crossing in the world, lots of shopping. Tokyo/Ginza as well, with the Imperial Palace. I'd highly recommend at least walking into a Pachinko Parlor!!! Be prepared for the sight and sound, it's intense! Yoyogi Park and Meiji Shrine. Fish Markets (go early to see it all in action - we went too late in the morning - did have great Sushi - be prepared for a long wait though). We loved going to the Sumo wrestling. (check if there is a tournament on - only 3 in Tokyo per year - otherwise there might be an exhibition tournament on).
I loved Asakusa - a bit older style Japan, and then the Koppabashi kitchen district. If you need a nice kitchen knife, there is a cluster of several stores selling Japanese knives.
All the food! Yakitori skewers of all types, Teppanyaki, Okonominyaki, Ramen, Rice Bowls, Gyozas, Izakaya, Sushi, Sashimi, Saki, Yakisoba.
We went to the Robot Restaurant... it was an experience... still not sure if it was a good one or not! ;)