There needs to be a plan to pay the line under a range of interest rates, and to pay it off.  

The offers I received for a cash offer (the property could not be financed) were in the $200,000 range.

You can easily find a turn-key property in the $250k range with cap rates around 6.

Assets identified in this study include:Appliances: Oven/range, dishwasher, refrigerator, washer/dryer, microwaveElectrical and communication systems: TV connections and dedicated equipment outletsCabinetry and CountertopsDecorative light fixtures: Sconces, pendant fixtures, chandeliersInterior Finishes: Crown molding, wood panel wall covering, window treatments8.20% of the total depreciable basis was classified as 15-year class life.

I also have a world class designer on my team that helps get these kind of properties from the average $60-$75k/yr range to over $100k/yr range (for 3bd homes; more the bigger you go).  

From cozy cabins to expansive luxury estates, there's a wide range of opportunities for investors here. 

- What are the best neighborhoods for buy & hold in this price range?

Start visiting building sites so you can meet the trades and see finishouts in different price ranges. 

I got snacks plus goodies from my favorite place Bath and Body Works!

Certain areas in Hayward and San Leandro could meet most of your criteria but they are in the $1M+ range.