I am considering putting a carputer in my 02 WRX and am wondering if it would be a good idea to have a 2nd battery.

I would be running the following on the 2nd battery:
Carputer
Rockford Fosgate P3001 amp for 2 10" Rockford Fosgate Punch subs
Another amp for all factory speakers

If I do this, should I mount a 2nd battery somewhere or will the single stock battery be able to handle it?

 

A computer alone won't draw all that much power. You should at the very least replace the stock battery with something better, an Optima would be your best bet if you plan to operate your equipment often with the engine not running.
As for having two batteries, you would not be able to do this with the stock alternator, as it doesn't have sufficient capacity to keep two batteries fully charged while running the electrical system as well. To do this properly, you would need a high-output alternator and an isolator.

 

I agree, the battery is only for standing still or running with the engine off -- your alternator should be handling 100% of the electricity generation for your car, period, PLUS topping off your battery. Repeatedly draining your battery again and again, even if it is a spiffy Optima, can't be good for it.

 

Actually the spiffy Optimas, particularly the Yellow-Tops, are made to do just that with no problem. The Yellow-Top is rated to withstand hundreds of deep cycles (full discharge), which is why it is used by people with high-power systems for extended engine-off use. Even the Red-Top is able to tolerate a limited number of discharges although not as many as a Yellow.

 

so where can you pick up a high output alternator like that?

 

some shops can re-wrap your current alternator.