So cracking open Humabaout's
Halfway to Anywhere spreadsheet and looking up brachistochrone transfers, I get a few travel times:
(for minimal distances, all from Earth)
For 0.5g, Earth to Mars is 3 days, to Jupiter 5 days, then Saturn, Uranus, Neptune take 10, 20 and 30 days respectively.
At full 3g, Mars is 1.2 days, then J/S/U/N are 3.3/5/7.2 and 8.9 days.
Since we've mentioned the Kuiper Belt: it's outer radius is around 50 AU, which is 28 days at 0.5g, or 12 days at 3g. So we could cross from one side of the occupied Solar System to the other in no more than 2 months. (I guess, that's based on 2 brachistochrone transfers via Earth, which may not actually be the fastest transfer path.) This is on a similar scale to modern Earth ship transport, where it might take 2 months to get from London to Sydney.