Unfortunately, for the time being, I do need to stay in New York.

If you close to the university, I might give them a call and see if they have a database that they use for places for visiting professors, etc can stay.

I’ll stay tuned to see what comes about about of your question though. 

The relatives are vacating. only 1 tenant wants to stay through ownership change.

If so, you may have less risk if you are comfortable with getting it rented / the MTR numbers.

The mortgage would stay under the seller's name.The buyer could then rent out the unit, renovate, etc. to increase cash flow or make more money.But aside from a possible "due on clause" being called by the mortgage company, what's the benefit to the seller?

A lot of family businesses cannot stay in business upon parent death due to no longer getting the prop 13 property tax discount.  

True that. 99% of people will stay on the internet, analyzing deals and doing research but when the time comes to pull the trigger on a deal they'll do absolutely nothing. 

If they haven’t been paying and causing problems why would you want them to stay?

Then you can rent in Seattle for 1 year or 2 to make sure you want to be there for a while and decide what area you want to live in and eventually buy something there if you decide you will stay.