From personal experience looking, I have found that a lot of Nassau & Western Suffolk duplexes need a decent amount of work (lots of old fashioned radiators from the 1970's in the photos!).   

Made a move into Radioactive Materials Remediation (I know weird move) and was hired by a large oil and gas company 2.5 years later as their Radioactive Materials Manager, learned explosives compliance along the way and spent my last 5 years there traveling all over the U.S. as their Corporate Radiation and Explosives Manager. 2017, Good Job, Good Pay, New Baby and then a heating fuel oil truck had a spill on my property and made its way into my home and under my homes footer, DEP got involved and to remediate it they had to tear down the house and we lost everything.

The heat is natural gas with cast iron radiators throughout the house.  

If it had radiator heat, that does make sense, but that too should have been recognizable to anyone that ever has been in an old building. 

We were thinking of installing an ecobee so we can monitor the usage, but I was just told that the entire building has radiators. 

However the entire centralized AC system is wired and  billed to the top floor ,the bottom floor has window AC unit and electric radiators, the AC vents in the bottom unit are freebies for the lower unit but they are controlled by the top unit.I have an interesting situation with as my new tenant downstairs doesn't like window AC.Even though it's relatively cooler downstairs the lower unit tenant has a higher demand for cooling than the top unit,this wasn't the case with previous tenant.Makes me wonder if the lower unit tenant wants to ride on my back to pay his unit cooling bill.

Does it have the big cast radiators  in every room also?  

In general: (1) I think we will need to hire a foundation company to seal the foundation, (2) I think we need to clean the place out & that will take a minimum of 4 dumpsters, (3) the flooring needs to be replaced throughout the house, we need a good flooring guy to go in and get that done, (4) the heating system needs to be replaced, (5) the radiators throughout the house need to be replaced, (6) the kitchen needs to be re done (new cabinets, new counters), (7) the bathroom needs to be re done, (8) walls throughout the property need to be finished, there is bare sheet rock everywhere, (9) trim needs to be added everywhere, (10) staircase rails need to be added, (11) the entryway needs to be completed, (12) front door needs to be replaced, (13) electric needs to be upgraded.

The kitchen measures 11' x 11', but there is a radiator along one wall which takes roughly 1' off, so let's assume 11' x 10'.

Upstairs unit which has no central air and radiator heat has been rented for over a decade by the same tenant.