I'm slightly confused about the metrics you're asking about, first is GRM and then cap rate/COC. Anyways sounds like you're mostly asking cap rate. I think here you want to be specific about property and location. Cap rate is used for >4 units while comps are used for <4. If you want to use cap rate for <4, may be inaccurate, but you might expect 6-8% depending on area with 9% and up if area is rough and you're willing to get creative with your deal. Midwestern cities like Minneapolis, Madison, Chicago etc will are equity markets similar to costal cities, while other midwestern markets are good for cash flow. Check out Marcus & millichap North American investment forecast for some info on good markets.
Sounds like a good idea about tapping into equity with a low DP option in CA, if that where you want to con't living, though if you plan to make this property a rental I'd make sure the numbers make sense before buying. To find a decent midwestern property, I think you'll be taking a major risk unless you spend 1-3wks in a city to feel the pulse of the local market & do some team building.