Market is pretty saturated right now, but you can still get a good deal if you move quickly enough when one pops up (if you're looking on MLS).

I think you can get an idea on how saturated it is by using AirDNA.co.

Agree-- Nashville is totally saturated. 

Or is the rental market over-saturated such that the lack of demand for rentals commands a lower purchase price?  

LA's a great place to do real estate and as most know we are over saturated with realtors here many who are under performing or not performing at all.

First it was Clarksville, TN for long term rentals ( LTR) then they decided (“they,” - out of state investors from WA, OR, CA) to move to STR rentals in Gatlinburg as an active income source.The pro of the decision is that rates are great in that area however it might be more saturated since its the “talk of the town,” along with all the other touristy places like the Pocano’s in PA or Palm Springs/Coachella, CA, / etc.However, from a high level approach you’ll want a high income activity or active income machine (for some this is a tech job, an actual business, or STR they operate) and then the passive income sources.

Is anyone in a market that they feel like isn't Saturated? 

Our final project is on the risk analysis of China using anti satellite weapons, our analysis shows that if they do it three times the satellite orbit will be saturated for 20 years.

Evaluate how saturated your local market is with rentals and what the going rates are compared to use.

Boise is a pretty saturated market, if you are looking for investments close to home I'd consider this side of the state.