Karma marks folks with a quick tongue....Watch what I say.
I have been blessed to find very very nice places here in Mo ...Now that I am trying to relocate I am finding it hard to find GOOD Houses..BUT many are struggling with possible foreclosures that many are accepting vouchers...Just ask around...try Zillow.com as well and just look around.
I hope you find something..if you need further help contact me at firstname.lastname@example.org and I can help you more.
I am not sure that there is much of a stock of 4BR/2 bath homes in good neighborhoods with great schools, though. Generally homes with those features can rent above the current market rate without the need for the landlord to participate in the Section 8 program (which sets the rate they can get for the home).
In other words, if I can rent my home for $1500 per month, and Section 8 will only pay $875 for the same home (through some combination of government contribution, and tenant contribution), it would make more sense for me to rent it privately.
Many of the features you mention would result in a home being able to rent above market rates (nice area, good schools, close shopping, 4/2). I am sure that is not what you wanted to hear, but it may help you adjust your expectations and understand the program from a landlord perspective somewhat.