Believe it or not, but downtown San Antonio which is a Major Tourist and Convention area, is pretty quiet during week nights unless something Major like Christmas, Fiesta or Battle of Flowers is going on.
The River Walk has lots of Bars,Clubs and Places to eat,but tend to be dead after about 11pm except on Weekends or if Major Conventions or Sporting Events are in town.
Since the Southbound Eagle arrives anywhere from 930pm till Midnight depending on the OTP,the River Walk can start closing before you reach it.
There are several Clubs/Bars on East Commerce close to the Amtrak Station but they tend to be quite too but are,OK for a Drink. There is also a B-B-Q place called Smoke close to the Station thats good. There is a 24/7 Dennys close to the River Walk on East Commerce also.
As for sightseeing, the Alamo grounds are closed at night, but it's Lighted and lots of Tourists are around till late.IF you do this,cross the Street in front of the Alamo and walk down the Walk into the Hyatt Regency River Walk. There is a Lighted Stream ( artificial) with Falls that runs into the Lobby and empties into the San Antonio River on the Riverwalk.
The famous Menger Hotel is next door, with the Bar where Teddy Roosevelt recruited his Roughriders.
If you like tourist stuff, you can go up to the top of the Hemisphere Tower ( like the Space Needle in Seattle) and get a good view of the Huge area that is Greater San Antonio lighted up @ night.
You might want to just stay aboard and sleep, which lots of people do, but if you do visit the River Walk, you can't re-board 'till they start boarding the Sunset Ltd. #1 about 215am after the Switching of the thru Cars from the Texas Eagle.
Hope this helps,nice trip!