Are there any areas that should be avoided and are there any steps I should take to protect myself from radiation?
An american software engineer living in Japan gives a good overview of how big Japan is and why you shouldn't be afraid to travel there after the nuclear accident.
Essentially, the summary is that Japan is very large. It's unlikely that your travel plans as a tourist will be anywhere near the accident.
I am living here in Tokyo and nobody worries much. Don't worry if your plane lands in Tokyo.
I don't have a Geiger counter but hearing from the local news, Tokyo seems quite safe.
Other places more in the south (Mt Fuji, Osaka, Kyoto, Nara, Nagoya, Okinawa) should be even safer.
You might just want to avoid the Fukushima area, even though going there for a day or two should be OK.
If you're worried, don't drink tap water, and avoid lettuce/leaves (actually those advices were valid 2 months ago but it might be overkill now).
Yes, of course there are areas you should avoid. However, most of Japan is completely harmless.
Here are two maps of the Japanese radiation, with frequently updated readings, both have the same data sources, mostly governmental:
If you do not trust the government, you can also check out this map, which is assembled by citizen measurements.
If you convert the nSv/h with a converter and check the famous XKCD Radiation Chart, you can see that the generally below 100 nSv/h values all over Japan are equivalent to eating a banana per hour. The higher value around Fukushima below 1000 nSv/h are equivalent to an Arm Xray or 2.4 times what you get normally during a day in average.
So you are not advised spending a longer time in the direct vicinity of the nuclear power plant. The rest of Japan, as background radiation is concerned, is no issue at all.
Regarding food, it basically comes down to the same issue, with the added danger of course that the food travels around the whole country. If you want to be absolutely sure, I would recommend you to buy one of the new very small Geiger counters that you can get for about 40USD which will be shipped to your Hotel in Japan without problems (and without knowing Japanese). However, one has to say that people in Japan are very concerned about radiated food. So you can safely assume that a large part of what reaches the supply chain or reasonably priced has been checked for radiation already. But of course, as history shows anywhere with food safety, this is not a 100% guarantee.
I just got back from Japan this morning and I went to both the Tsunami area where I volunteered for cleanup which I recommend to everybody, and on the way from there to Tokyo I passed through part of Fukushima though not close to the nuclear plant. Everything seemed like business as usual except there are fewer tourists in many parts of the country and in Tokyo my hostel was unbelievably cheap.
Travelling to any areas in the south west such as Kyoto, Hiroshima, Osaka, Okinawa, etc. are still okay as of this date. However, I'd stay away from the Tokyo area and anywhere more north of that (such as Fukushima). The levels I hear (from family members in Tokyo) aren't too bad if you are only there for a few days, but if you are living there, then the levels may not be healthy.