This month I had a tenant turnover so with cleaning and the screening of the new tenants, the old tenant referred the new ones to me, I will spend 3 hours total time on this.

Better just let your property management company deal with it in their system and spend $100 on labor while you sleep peacefully.

This is about the ceiling for what we are looking to spend out of our own pockets. 

I have excess earnings after expenses and my accountant advised to spend this cash on a property, vehicle, or 401k to avoid paying taxes on it.

Spend a day in each area and drive around to learn the areas, the local traditions etc.  

The issue is that Newburgh is at least 66 miles away which would multiply the amount I spend on gas monthly and also tolls, not including the hours off of my life that I would spend traveling. 

I don't know your total spend but my cost for new SFH construction is up about 30% this year.

I can think of better ways for you to spend $50-150 per month if you are just starting out.  

I was working 60+ hours a week at my W2 and didn't have a whole lot of extra time to spend hustling.

Start saving as well and spend every free minute you have on MLS or even realtor.com and Zillow if you don't have access and start learning, seeing what the market has to offer.