There are a lot of horrifyingly terrible stations in Texas. Taylor, McGregor, and Cleburne all have terrifyingly substandard platforms, although some of them have OK waiting rooms. Malvern, AR is another failure-of-platform. It was an eye-opener for me to ride the Texas Eagle, because the routes I'd ridden before all had proper platforms.
Haven't seen them personally, but Alpine and Sanderson are awful too.
Sanderson is probably the worst in the system. Beaumont used to be worse but they finally replaced the platform.
Houston is probably the worst station which is located in a top-10 metropolis.
There are also a number of appalling SEPTA stations on the Northeast Corridor -- asphalt patches at the side of the tracks, with grade crossings to board trains running on the inside tracks -- though SEPTA is slightly outside the bounds of the question. Most of these are being upgraded to real platforms as SEPTA gets money.
Best? Honestly most of them are pretty nice.
Denver is probably the nicest one I've been to.
Of the ones I've gotten on or off at... St Paul, LA, Philadelphia, Boston, Syracuse (my home station), Utica, Albuquerque, San Diego, Worcester MA, New Rochelle, all very nice.
...Salt Lake City is an oddity. Amtrak is in a temporary building which is a bit of a shack, but it's located on the corner of a very nice open-air intermodal facility. And the *platform* is all spiffy and nice. So on the whole Salt Lake is a very nice station, though the Amtrak building is the shabby end of it.
Kansas City is nice except for the *extremely* long walk from the ticket office to the platform.