Two counter-examples, although admittedly from a time ago.
Kalispell Montana, where the train station was almost to the north edge
of the city at the time. Whitefish Montana where it was also to the
north edge.
Lon "Both, conveniently located along the tracks" Stowell
With Amtrack budgets being what they are, may stations have moved
outward as older facilities got knocked down, gentrified, or re-
purposed. Tacoma's station, Worcester's station, Springfield's (1)
station went from Palace of Mobility to oversize doublewide like this,
for a few offhand examples. The locations were often not convenient.
Some older facilities retained weren't the best sited among the local
options, the old Amtrak station for Oakland, Ca being a real case in
point. Anything that can make other parts of Oakland look good by
comparison...
Anthony "(1) the real one, in Massachusetts, of course" McCafferty
Can't speak for the others, but Worcester's Union Station has been
rehabbed and is back in service.
pt