You can buy nicer rent-ready properties that will attract higher quality tenants and have a good property manager managing the property (5 minutes per year time spend), or you can buy a total dumper that needs rehabbing and then you can landlord it yourself (up to hundreds of hours of time spend).

inherited" tenants like yours are probably waiting to hear from you, so send out contact emergency info and have them respond and include with next rent payment a updated contact sheet,, I'd make an appointment to tour inside of each unit with condition sheet,, the condition from your date of ownership is now what you use for condition move out.. so once that's completed you now know which unit would be tops on your list to rehab and offer an early out to.. if that's a consideration.. you can of course let all tenants know the rent will increase to $$$ when their lease is up and you are accepting 30 or 60 day vacate notices early, they'll be prepared. 

It has been many years but tax is not increasing much. 

Make friends increase your circle of influence - Hire a private detective - they are good at finding people (give his a piece of the profits)Check the death notices or search government record for certificates of death, check the obituary for next of kin - contact them. 

HiI recently became highly interested in becoming an investor, as it seems an attractive retirement plan.

I believe this will serve to be more attractive to potential tenants and I will most likely not have to incur any maintenance reasons for hopefully several years.

A 3-5% increase in that price range is around $25-$50 a month give or take.  

There are two to three markets I am interested in that I have some small relationships within that I could utilize, my hometown, my wife's hometown or a place I visit often for work.My questions concern the opportunity cost of learning the ins and outs of 3 different markets when the requirements of truly knowing the market increase the chances of success.Do I select one based on distance, the potential to cash flow or appreciate, or one that I may have more connections in?

I want the tenants to move out solely because the place needs a major renovation and subsequent rental price increase.

If you're personable and passionate, you will attract enthusiastic people.