Westport is waaaay more trouble to get to from downtown than it's worth, imho, depending on your party style.
Union Station (not Grand Central
) is a shopping mall/center with the hotel and restaurants and such attached to it. On one end is a MetroLink station (Metro is our moderately useful transit system). From there, you can easily get to Laclede's Landing (just next to the river), which is a historic district with lots of bars and clubs and such.
That option saves you driving or getting cabs (it's like $1.50 to ride metro, as opposed to trying to find a cab in our cab-draught city, then paying $40 to go 6 blocks)
If you feel like going off the Metro route, you can get to the Central West End (about 10 minutes from Union Station, safe, trendy/large gay population, nice coffeeshops), Washington Avenue (about 5 minutes from Union Station, not as safe, lots of clubs and bars), the loop (About 15 minutes from Union Station, hip shops, bars, and people watching, reasonably safe), or , yes, Westport (about 35-40 minutes from Union Station, yuppie, chain restaurants, comedy club, etc, very safe, very white).
Union Station
The Loop
Westport Plaza
Central West End
Wash Ave
Laclede's Landing