When to use "hit" instead of "go"

Solution 1:

It's a shortening of hit the trail, or more recently hit the road. Here's a chart showing how common these expressions are for leave, get going.

In these usages, hit primarily refers to physical contact between your feet and the trail/road, but figuratively, horse's hooves/car's 'boots' (tyres) can make vicarious contact for you.

As @bracho monacho says, it's impossible for us to know whether the speaker simply meant he was leaving (hitting the road), or going somewhere to sleep (hitting the sack). If he was intending to sleep, it's quite possible the speaker himself didn't really care which meaning he was shortening.

Solution 2:

Are you sure the person didn't say "I am hitting it now"? The phrase "hit it" is a colloquialism that means leave or depart. It may be a shortened form of "hit the road".