It is possible that over time, Google ranking metrics recognize the uniqueness of your key words, and you move up in the rankings organically (without a cost to you), so that you can be found easily on Google searches for your location.  

If you treat the renter (resident) well, provide a well-kept home that you service regularly, and stay on top of any maintenance issues, a resident will likely remain in the house for many years. 

I did some research and saw reasonable prices on following neighborhoods, after I read what you wrote I understand that the good prices might have been on the less good side of the neighborhoods but not sure how to check.if you could let me know if it is better to stay away from some of them I would really appreciate It:Mount Washingtonverna- out side of Pittsburgh BrooklineLarimerLincoln PlaceCarnegieWilkinsburgHazelwoodSherade

It's important to stay informed about developments in the areas you're considering, as well as any potential changes in regulations or economic conditions.

Just personally, I would never do an absentee landlord kinda thing....Too many moving parts, too much to go wrong and cuts into your profit big-time....Sentimental value is one thing, but not if you end up hating the house down the road.....Stay local, plenty of opportunities in good ole AZ.....

@Amir Portal  I think you should stay open to all areas. 

We had hoped to rent our house for short-term or mid-term stays.

We want to acquire a property in one of these areas, not only as an investment but also as a place where we can stay when we visit the United States.

I would also weigh if you plan on staying in the home you are in now for a long time or move in the next 5 years.

Are you looking to stay in the city?