I strongly recommend buying a rail pass for traveling to Tohoku. It is about 19000 yen for a 5 day pass, which means you can pick 5 days to use the pass within 14 day period. For traveling inter-cities, you have to use Shinkansen but the ticket price is very high. JR pass really saves you a lot as a one way ticket from Tokyo to Aomori already costed you about 20000 yen.
In addition, you may reserve tickets on internet to secure your seat on train. Otherwise you have to go to non-reserved carts to find a seat. The reservation of seat can be done via JR official website or a website called ekinet. For foreigners using English, you can reserve your seat before the date of departure but you have to pick up your reservation ticket 9:00pm before the date of departure. Hence, it poses a difficulty if you want to travel on the date you arrived in Japan. However, if you use Japanese website, you can pick up your reservation ticket before your actual departure time. So......is it racial discrimination?