Also, who says the OP has to pay for lodging at all when they get to their destination? Just a thought.
Well I suppose if you don't want to sleep in LAX you'll have to find a place. And even if it were the case-- if you're concerned about money the plane will still be cheaper.
If you're staying with family or friends, you don't have to pay for lodging.
Here's how I break down the comparisons for a round-trip.
If you're only comparing taking the train and driving, and not considering flying, then you should look at:
getting to/from stations (and parking if relevant) + train fare (including accommodations) + food + lodging, and days of transit
automobile costs (gas + depreciation/maintenance) + food + lodging, and days of transit
Running that calculation, the train will almost always be the cheaper of the two. For me, two people traveling, the comparison would look like this
SEPTA tickets $18 + Amtrak roomettes $1600 + food $0 + lodging $0 + LA pubtrans/taxi $32?, 6 days transit = $1650, 6 days
Intangible advantages to the train: not driving, socializing opportunities.
5422mi*.55/mi $2980 + food 60/day*10days $600 + 80/night*8nights $640, 10 days transit = $3020, 10 days
Intangible advantages to driving: being able to take detours, visit museums, eat local cuisine.
So, it comes down to how you rate (saving $1400 and 4 days, not having to drive, socializing) against (flexibility in itinerary, more local experiences).
If you're comparing taking the train and flying, then it's a totally different equation. It still has multiple numbers to look at, though:
getting to/from stations (and parking if relevant) + train fare (including accommodations) + food + lodging, and days of transit
getting to/from airports (and parking if relevant) + airfare, days of transit
For me, two people traveling would look like this
SEPTA tickets $18 + Amtrak roomettes $1600 + food $0 + lodging $0 + LA pubtrans/taxi $32?, 3 days transit = $1650, 3 days
Intangible advantages to the train: not driving, socializing opportunities, seeing the country, relaxing.
SEPTA tickets $28 + airfare*2 $800 + LA pubtrans/taxi $32?, 1 day transit = $860
Intangible advantages to flying: none, in my opinion, and disadvantages of comfort and jet lag.
So, it comes down to how you rate (socializing opportunities, seeing the country) against (saving $800 and 4 days, with two days of discomfort and jet lag).
A bigger question: do you have a fixed amount of time for a vacation you're trying to fill (14 days total) for transit and destination time, in which case you get either 12 days in LA or 8 days in LA? Or do you have a specific amount of time you want to be in LA (say, 7 days), in which case you're comparing 9 days away from home with 13 days away from home? Those are two very different situations. IF THE FORMER--if it's a 14 day vacation either way--THEN you also have to consider food and lodging for those additional 4 days of your vacation that are in LA when you fly. Add to the cost of flying food 60/day*4days $240 + lodging 100/night*4nights $400 = $640. That cancels out a lot of the cost savings!!! But that doesn't apply if your time at the destination is fixed.
Additionally, if you have to drive to and park at the airport but don't have to do that for the train, of course, you have additional costs. My parents, for instance, would have to do that, so they would be paying something like $10/day for their entire trip to leave their car at the airport, whereas they could park at Kemper St Station for free. That might cut $140 off the savings for flying, for a two week trip.
So, for instance, if my parents were to take a 14 day vacation, the train and flying would cost pretty much the same. The $800 cost savings we worked out at first get reduced by $640 and $140. Then it's only a question of intangibles, not cost. 6 days on the train, or 4 extra days in LA but 2 days of airport/airplane discomfort plus jet lag?
There's no easy answer that fits everyone!