LA is gonna get a team at some point, possibly two. The NFL more or less have a pretty good geographic based on division process. The only team that really doesn't fit is the Dallas Cowboys in the East, but that's to keep their rivalries with the Redskins, Giants and Eagles (mostly Redskins).
Oh, and the Colts are in the South, but other than that, everything's pretty good geographically.
LA is looking at seven franchises. In order of likeliness, they are the Jaguars, Bills, Vikings, Chargers, Raiders, Rams and 49ers. Los Angeles would preferably play in the West, so they could have a rivalry with the Raiders/Chargers or 49ers/Rams (Seattle and Phoenix are rivals in other sports as well, so that fits too).
LA could conceivably play in the South, but that's not too likely cause it's not really in what we define as the South (east of Texas). I know they definitely won't want to put it in the North or East, especially as a market that has a lot of potential for good rivalries with nearby squads.
Here's what I think will happen for each possible movement:
1. Jaguars to LA: Just keep them in the AFC South. The only AFC West team that could really be bumped is the Broncos. No one is getting rid of the Chiefs/Raiders rivalry. The Broncos don't really fit in any other division, especially as the North is dead set. Another option would be for a team to switch conferences. Panthers to AFC South, Cardinals to NFC South, LA to NFC West.
If Los Angeles Were To Bring In A Team, Who Would It Be?
2. Bills. I have no clue how they'd fix this one. An LA team playing against two Northeastern teams would be ridiculous. The most logical option would involve moving the Ravens. But that would ruin the Ravens/Browns as well as the Ravens/Steelers (that part would get replaced by the Patriots, though). After that, the Broncos could be sent North and LA could be in the West. Or the Jaguars could be sent East and LA could be South (see above).
3. Vikings. Just put the Rams in the North to keep up the whole Midwestern theme, LA in the NFC West
4. Chargers. NOTHING TO DO
5. Raiders. NOTHING TO DO
6. Rams. NOTHING TO DO
7. 49ers. NOTHING TO DO
Several teams will leap up for the opportunity to move to LA. The NFL gets the final say though, and for the reasons mentioned above, I'd see them taking a Western team first if all things are equal.
This way the least amount of teams will have to be shuffled around. Every division is rivalry heavy and some (AFC North and West, NFC East) are so perfect you just can't mess with them.