I need to add a circuit breaker and 3 or 4 outlets in my garage, preferably a non-GFCI circuit. I suspect it will be easier to run conduit around the walls than to try and run wires behind the already existing drywall.

Anyone have experience doing this yourself? Or is it just better to hire an electrician to do it, so I know code is met?

I think code requires gfci in garages now

Can you access above your garage....maybe an attic up there?

Garage is directly beneath second story.

I have a refrigerator that pulls more amps on start-up than the GFCI can handle.

I would run 12/2 wire up threw the ceiling and use fish tape to pull it down to were you want it. Should not be that big off a deal. Is there a crawl space. to the 20 amp ground fault plugs. And put in a ground fault breaker.

An overloaded circuit has nothing to do with it being GFCI. GFCI detects ground faults, it doesn't trip on amperage.

If you cannot access the space above the garage then I would run conduit.