Depends on the show and the venue.
Example - no one's going to meet them backstage at SXSW, unless they won passes from a radio station or something. Festivals aren't the place to meet bands.
Same goes for very large venues - though it's not always the case. You have a better chance of meeting them after they play, say... Chicago's House of Blues than you do after they play Madison Square Garden. (Though I did meet them at Pitts. Mellon Arena once, and that's a large venue).
Your best bet is hanging out by the busses at a small to medium venue - so long as everyone's in a good mood, the band usually comes out an hour or so after showtime. Scott likes to take a long shower afterward.
However, on the last tour ('08), a lot of people reported that Scott was just going from the venue straight to the bus, and not stopping for autographs or photos. Maybe they caught him on a bad night. Eric also likes to head right for the bus - I'm sure a little R&R is needed for all the boys after a killer performance.
Depending on your city, you may be able to track the band down the night before or after a show at the very upscale hotel chain they like to stay at. Cleveland's a small town, I don't have a lot of options here. In a place like LA or NY where there are 50 different Ritz's, I don't know so much. Hone in on your stalker skills.
I've had the unbelievable luck and complete pleasure of meeting the band several times, mostly on their Sex and Violence tour when OCM and I followed the band around half the country. lol. They're a great, amazingly friendly and sweet group of guys - a class act all the way. Best of luck!