Jon Lang wrote:

If I have accelerations that let me travel a parsec in a month, then I
have enough acceleration to go anywhere in the galaxy in 20 years.
Barring navigational hazards, of course: there may be a practical top
speed based on the density of the interstellar medium - if you go too
fast, even that near-vacuum will be too much to handle.

Why deal with acceleration to start with? At a minimum, any such drive should pay for the potential energy differential between two locations, and that will just apply a speed limit that depends on the local slope of space (i.e. is inversely proportional to the local gravitational field). At 1 kW/kg, which is a reasonable power density, escaping earth (potential well: 62 MJ/kg) takes 17 hours and your surface velocity is limited to 100m/s, escaping the sun (potential well: 860 MJ/kg) takes 240 hours and your velocity at 1 AU is limited to about 160 km/sec, and reaching a nearby star is actually quite cheap in potential energy terms but may still have a velocity limit.
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