Raising the rent too high could lead to undesired confrontation and may be difficult to find tenants moving forward if the current tenants choose to find housing elsewhere.

She is a single Mom who has had an undesirable "boyfriend" hanging around for several months. 

It isn't that sub-30k properties are undesirable, but looking for them in high crime areas will make your goals very difficult to achieve.Think of it this way: imagine you're a higher quality housing choice voucher holder.