I got a quote of $5500 for installing a 80% efficient American standard gas furnace, a 13 seer 3 ton air conditioner and a digital thermostat.

I don't know about the thermostat anymore, I have had bad luck with my Nests getting fried. 

We've renovated our student housing to be more efficient (programmable thermostats with a max and min temperature preset); LED lighting (fixed, not LED bulbs in traditional fixtures); low-flow toilets and faucets; HE laundry units and humidistat controlled fans bathrooms.  

Another benefit to the 90% is the marketing talking point of UPGRADED hvac ;)We went with a "standard" 80% furnace for the upstairs to save a little cash since it was easy to vent.Something else we started doing this year is installing Wi-Fi thermostats.

AC stuck in a cycle or inoperative thermostat?

This assumes your electric panel can even support electric heat, which is unlikely.My advice is install landlord thermostats that limit the maximum temperature or install wifi thermostats that you can monitor.

Another good question is where is the thermostat?

The main things that will break or need replacing are the agitator dogs on washers and thermostats on dryers. 

Our latest.. the tenant decided to install a nest thermostat at one of our better rentals.  

However the thermostat is located on the main floor and it controls the temp for the entire place.