I took a chance on her and she turned out to be one of my best tenants ever - she paid rent on time, kept the apartment in immaculate condition, decorated tastefully on holidays, and went above and beyond to maintain common areas. 

Realize that it's going to be hard to find a tenant, hard to collect the rents, a nuisance to maintain, and risky in every sense of the word. 

As an out of town investor how do maintain your property and make sure it doesn't turn into a drug den without hiring a full-time on-site manager?

In most states it only costs a few hundred dollars a year to maintain an LLC and so long as you respect it as a being separate and apart from yourself, you should be able to shield your personal assets from any exposure and sleep better at night.

This is beyond the City's powers and so the property basically maintains it's status unless it's destroyed. 

I am eager to learn more on how to maintain my property and maximize my profits.  

These are not assets for a street level investor nor would any street level investor qualify for the management requirements let along the capital requirements with some of the smallest pools being north of $30 Million.In certain HUD sales, like those pools with NSO loans (Neighborhood Stabilization Outcome) management/administration has a duty to treat loans in the prescribed manner and must maintain reporting post sale for a year or two.  

I'm sure it will help me maintain any rental properties I may acquire until it comes time to hire a property manager as well.

Not the poorest of areas, definitely not the wealthiest of areas, the large local grocery chain still maintains grocery stores there, starbucks/wal greens can be found etc.2 shopping centers, one free standing office building, 3 other mixed use properties that have restaurants, retail and office space.  

Clearly, a new build or very well maintained property would require less monthly in repairs, but these often sell at a premium.