It really depends on what level of acceleration you're comfortable with.

$$distance = 0.5*acceleration*time^2$$

So assuming you spend half the time accelerating and half decelerating then in 3 hours you could travel a maximum of ~58'000km times acceleration in m/s (or ~gees/10). So 1g (well, +1g for 1.5hrs and -1g for 1.5hrs) will get you around 580'000km (and a peak speed of 53km/sec - easily enough to leave Earth well and truly behind) while 0.01g will get you 5800km (and a top speed of ~2000kph).

This of course says nothing about comfort, power consumption, (sonic booms, escape velocity) etc.

It really depends on what level of acceleration you're comfortable with.

$$distance = 0.5*acceleration*time^2$$

So assuming you spend half the time accelerating and half decelerating then in 3 hours you could travel a maximum of ~29'000km times acceleration in m/s (or ~gees/10). So 1g (well, +1g for 1.5hrs and -1g for 1.5hrs) will get you around 290'000km (and a peak speed of 53km/sec - enough to leave Earth well and truly behind) while 0.01g will get you 2900km (and a top speed of ~2000kph).

This of course says nothing about comfort, power consumption, (sonic booms, escape velocity) etc.