Hello Cielnoegao!
I have been living in Tokyo for about a year, and from my experience I can say that overall, my experience as an expat has been great.
Socially, problems are very rare. Most people are tremendously welcoming and eager to both learn about your culture and teach you theirs. In Tokyo especially, though, when people are out in public, it is accepted most of the time to contain your emotions, and not make a scene. So even if someone does harbor some resentment as you accidentally block the subway entrance or some other typical foreigner mistake, or they just don't like foreigners in general, their culture is often stronger and they will not yell, stare, or even make you aware that they disapprove. Occasionally you will come across restaurants or bars that do not allow foreigners in, but often these establishments are sleazy or nasty, and you wouldn't want to go there anyway.
However, I have had a few female friends, especially foreigners, who said that they have had problems with being followed by some Japanese men. I had one friend from India say she was followed onto and off of the train, to where she worked, and he would occasionally follow her around and try to talk to her off and on for a couple months. Tokyo is a very busy and well lit city, and it is very easy to stay in public and around large crowds if this does indeed happen. In addition, in Tokyo there are many many small police stations called "Kobans" with at least a couple officers inside, and if you are being followed and feel uneasy you could walk into one and tell them.Â
As I said, the Japanese I have met have been very welcoming and willing to help me out when I run into problems. I believe that much of the anti-foreigner sentiment tends to emerge when it comes to long term commitments. For example, many Japanese companies do feel an obligation to hire Japanese first, but there are those that work internationally and are in need of foreigners. Also, dating is often quite easy for foreigners, but long-term relationships can cause strain because often parents want their children to marry only other Japanese. I think this is more because of a desire to maintain their Japanese culture than anything else. But in the end, its a huge country with so much to see and do, and problems are rare. I was greeted incredibly warmly and given a lot of help when I took a trip north to Akita. It has been really hard for me to have a bad time!