If we take the figures from 2011 as an example, we can see that almost 17 million people chose to take a holiday outside Japan (these are figures only for people who used their passports, so we don't know how many people chose to holiday at home or which destinations they chose). Among those, the favourite destination for Japanese travellers was China. More than 3.5 million Japanese visited China that year, with almost as many opting for Korea and then the US, especially Hawaii. You can see the top 10 countries here.
However, in the next few years the figures may look different. In 2012 it was noticed that package tours from Japan to China had dramatically decreased - by almost 80 per cent. This was thought to be largely due to some bad feeling between the two countries caused by a dispute over islands that both countries claim to own.