You can easily spend 3 days in Tokyo and still not see all the highlights. As for places to eat I cannot provide any specific recommendations as I pay little attention to where we have eaten. In general the more traditional restaurants/ places to eat will do 1 or 2 things and do it well, wether is be ramen, sushi, yakitori, tonkatsu etc. some will also specialise in one thing only e.g. eel, chicken, beef. The more traditional restaurants are also small in size compared to western establishments some may only sit 8-10 people, in general if there is a queue it is normally pretty good. Queues can move quite quickly as the guests order, eat and leave and do not hang around. A food tour may be a good idea however I have not done one of these.
Getting around in Tokyo is easy and cheap but it may take a little getting used to, purchasing tickets for the JR lines and metro is easy and all the machines have multiple language options. If you need to change lines the biggest trick is making sure you stay within the station on the rail side as if you exit the station you may end up having to purchase another ticket. Also when entering the train stations ensure you hang onto the ticket as you need these to exit. If you purchase a ticket that doesn't cover the actual cost don't worry as there are adjustment machines inside the station. The use of IC cards such as Pasmo or Suica can be helpful but maybe not worth it for 3 if you are not planning on going back any time soon.
As for some of the essential sites most tourist will make their way to the Shibuya crossing, it is outside the station and always busy and if you are in the area Harajuku is just up the road. Shinjuku is another major center and is only a few stops away from Shibuya. Ueno and the Ueno Park area has a few good museums as well as a number of back streets that are worth walking through. If cooking is your thing from Ueno you can use the metro or walk to Kappabashi St (kitchen St) and you will find everything you could ever imagine in relation to kitchen stuff. In that neck of the woods there is also Asakusa with markets and the Asakusa Shrine. Akihabara is the electronics and gadget area of Tokyo and then there is Ginza. You can easily spent 3 days in these areas alone and you will not have ventured from a 3-5km radius of central Tokyo. You could do a day trip down to Kamakura which is on the coast as was be capital of Japan for around 150 years back in the C13. If you really wanted to you could take a longer day trip to Kyoto (2 hours on the Shinkansen and for some will be considered as not inexpensive) or another major city out side of Tokyo.
Having been to Japan on a few occasions I find it difficult to provide recommendations on what to see and places to go to. Each time we go we list out the places we would like to see and then drop a few off the list. Anyhow have fun and I am sure you will enjoy your trip.
