you can also look into lower down payment options, like a house hack, or a seller finance deal. 

You might benefit from house hacking vs. doing full STR while you are away.

Some investment strategies like STRs may be barred or house-hacking even.Condos may tend the limit "highest and best use" maneuvers.  

I'm looking into potentially house hacking a small multi-family home, preferably in northern NJ (such as Morris county) or Westchester, NY if possible, but I'm open to other areas that are hopefully within about 1.5 hours (driving or public transit) of Manhattan.

House hacking is such a great idea for your first rental and gives you a lot of flexibility.  

If you don't have a primary residence yet, I would highly recommend house hacking first.This is a great strategy to use low money down, get into an investment property, have a roof over your head and still keep a large portion of that inheritance. 

I house hacked my way into my first rental property this past year and now manage the rental myself. 

Assuming your financial situation hasn't changed, if you are refinancing to a lower rate, I'm not sure why you need the house hacking income.

Best bet would be if you could move to Lehigh Valley and house hack there.

For example, if you start with a big single family home in the suburbs, then want to hack a 4plex in Minneapolis the following year, there will be questions regarding your true intention to occupy that 4plex as your primary.