My town actually has an E.R. and urgent care. We have a CVS in town too (my town has a lot of stuff!!). There are also medical taxis (there are no regular taxis here) and private hire ambulances that'll take you if you need a different hospital.
Typically you get the number of the closest general doc to you, and make good friends with your neighbors, so somebody can drive you to a hospital right away if you cut your leg off in the middle of the night. Could be a long way off or right around the corner, it depends.
The biggest thing I never anticipated? Car parts. My brakes went and rather than bring it to the local mechanics I tried to fix it myself. Walk into town takes about 40 minutes, getting the right parts took weeks.
Power also went in the spring due to freezing rain bringing down trees. Cell signal went, along with power and internet, and my water well's pump is electric; heat is propane but the damn heater's thermostat went, probably electric too. So being prepared to be off-grid once a year is useful.