Being the cheap local bastard that I am, any recommendations on which hotel to park my car for three week out of town trip. (Instead of getting cab or parking at airport). TIA.

MGM Grand has a large garage and a close ride to the airport.

For really free parking, the park and ride lot for the south terminal, you can probably leave it there and they shouldn't care that you're gone.  Gillespie just south of Sunset Rd.

Bob

I would be willing to bet that Bob would rent you a parking spot for a nominal fee. Right Bob?