There are 16 properties under $200K for sale in all the cities you mentioned.
Note that in addition to the purchase price, you should also factor closing costs which can vary depending on the city's transfer taxes, HOA transfer fees, etc if applicable
Do you have a realtor helping you? If not, that's the first thing you should do -- engage someone to help you find the properties to meet your needs.
I have another client in the same position --- unfortunately, not all the properties that are in his budget range meet his approval. You should consider making some allowances regarding the size, location and condition of the properties. Setting very high expectations may not help in a very competitive market that includes many cash buyers.
Let me know how I can help