My new estimates assuming 30mpg, $4 gal and a few hundred on maintenance
Ok, that's $0.13/mile
What you seem to be ignoring in your calculations is depreciation, generally the second highest cost-per-mile-driven after gasoline. I have no idea what you paid, but let's use MMM's "ideal," where you paid $5,000 cash, no interest, nad you can get $100,000miles total. That adds $0.05/mile. If you want to add how much you bought your car for, and how many miles you expect it to last, I can give you more accurate figures.
Tires, oil changes, fluids brake pads etc. will add another $0.01-0.02/mile. That's assuming you do all the work yourself. Total cost per mile will likely be above $0.20/mi. Probably near the $0.25/mi I estimated. I'll give both (low and hi numbers)
Let's move on and run your numbers.
For all of these, I'm quoting annual amounts assuming you commute a typical 265 days/year.
Old Job
$2.4k with $1.2k@ 31mi day @ 250 days/yr
commuting costs:$1,643 - $2053
New Job
$4.2k with $3k for work @ 83mi day @ 250 days/yr
commuting costs: $4,339 - 5,499
Hypothetical New Location
$2k with $800 for work @ 20mi/day @ 250 days/yr
commuting costs: $1060 - 1,325
Total savings of $2200 per year, if I live 10miles away.
Total savings
(low) - $4,339 - 1060= $3,279
(high) - $5,499 - 1,325 = $4,121
Conclusion:
$180 more on rent a month would break even and whatever my time is worth to add to rent
realistically, you'd likely save $343 every month moving closer. More if your car cost significantly more than the $5k I theorized with, or if you won't do the maintenance yourself.
here's a thread you might want to read:
http://www.mrmoneymustache.com/2011/10/06/the-true-cost-of-commuting/Just trying to show you some real-life numbers.