2k will sort you for about 2 weeks.
I can never get a plan for a Japan trip inside of that, it always works out massively more money than doing the same in the USA.
I guess you could spend 2 weeks on some bodies sofa or something for that but it hardly counts. I would like to do Japan but it just comes out at silly money each time so I always end up back in the USA.
And that's going with the girlfriend, which significantly reduces the per person cost as you have have 2 to a room, 2 to a rental car etc.
To be honest 2k for a months solo travel is really very little indeed unless you spend it in ultra cheap hostels or something or don't bother moving around much.
Would look at cutting it down to 2 weeks.