As a St. Louisan (but a transplanted Steelers fan, not a huge fan of the Rams), I can say that the old Rams - 49ers rivalry is rather dead, and since the Seahawks were an AFC team before the realignment to 8 4's, there is little true rivalry there....
St. Louis actually feels a strong affection for Kurt Warner. His life story has been so compelling, and he still returns to St. Louis regularly to do charitable work (often with a press black-out, since he doesn't feel a burning desire for publicity, but still word gets out regarding all his good deeds). So where St. Louis had a love / hate relationship with their old team (the Cardinals), many many St. Louisans want to see Kurt succeed, especially if the Rams aren't competitive (as has been the case now for 5+ years).
When the Rams relocation was approved in 1995, there was a stipulation that they would not contest where the league placed them in any realignment. They stayed with SF in the NFC West, as "'non-west" teams Carolina, Atlanta, and New Orleans were moved to the newly created NFC South. Not sure if they have a right to complain should the NFL see fit to shift them again.
Should the Jags move to LA, I would personally like to see St. Louis take the jags spot in the AFC South.
Indy, Nashville, and Houston would make decent geographic rivals.... The baseball Cardinals have a rivalry with the Houton Astros, Indy is just 4 hours down I-70, and the St. Louis Rams one moment of glory was vs. the Titans in SB XXXIV.
Obviously, Jacksonville is a very small market, and the Jags have fallen on hard times and RIGHT NOW would be a candidate to move. By the time a stadium is built in LA, Jacksonville could be back on top...
The Rams have an option to break their lease in St. Louis after the 2014 season, if the stadium isn't "among the top 25% of NFL facilities" (which it will NOT be, due to the plethora of newer, more palatial stadii). Some improvements were made this past year to the Edward Jones Dome (skylights, more video stuff), but I suppose without a reetractable roof, the place isn't quite as "competitive" as a brand new structure like the Jerry Jones Monstrosity...
Rams ownership may / may not undergo upheaval VERY SOON. After Georgia Frontiere died, her two children Chip & Lucy inherited Georgia's 60% ownership stake. They have explored selling the team, and 3 groups are reportedly submitting proposals. One is led by St. Louis Blues owner Dave Checketts (although he is NOT the big money man, Ruch Limbaugh WAS, but has reportedly been replaced). Checketts would likely keep the team in St. Louis. Not sure about the other 2 groups. Much of what transpires may be driven by tax implications of sale / non-sale.