JR East operates almost all trains for the eastern portion of Honshu. That encompases all the area from Tokyo region to the northen tip of Honshu (the main island). However the line that runs through Misawa recently changed. It is now operated by Aoimori Railroad.
Shinkansen is the Japanese name for the high-speed "Bullet" trains
The Tohoku Shinkansen runs from Tokyo to Aomori. It stops in Hachinohe and you can get connecting trains from Misawa to Hachinohe once or twice per hour.
Downtown Tokyo is now only three hours away. You could get the first train from Misawa at around 6:30 in the morning, spend the day in the city, catch the last train from Tokyo at around 8PM and be home by midnight. It costs about ¥29,000 round trip from Hachinohe all the way to Tokyo Station.
Purchase tickets here in Misawa before you leave. You should get three tickets (Misawa to Hachinohe, Misawa to Tokyo and Hachinohe to Tokyo).
Take the train from Misawa Station to Hachinohe Shinkansen Station. At Hachinohe, head up the steps and follow the signs. At the turnstyle feed all three tickets into the ticket reader. The machine will only give two of the tickets back to you. Then follow the sign with the bullet information. If all else fails show your tickets to any of the attendants and they'll get you to the correct track. A final note; If you are a non-smoker, be sure to tell them that when you buy your ticket. They have smoking and non-smoking cars.