CityWoman said:
What stove would any of you recommend to someone who doesn't want to carry propane with them on the road?
The Coleman 2-burner stove mentioned uses liquid white gas. You pump the fuel tank to pressurize (and can release the pressure when done). There are a wide variety of backpacking and car camping stoves that burn white gas. Fuel widely available and can be purchased in quart or gallon metal cans or plastic containers.
A lot of boaters use diesel stoves. 'Cause they have diesel engines, so they only carry one fuel.
There are kerosene stoves, both backpacking and kitchen. They are harder to start. Burning kerosene can have a slight smell. It gives me a headache in an enclosed area. Kerosene evaporate very slowly so don't spill it indoors.
Some backpacker stoves use multi-fuels: white gas, unleaded gas, kerosene. Again, you provide the pressure. Great when you don't know what fuel will be available. Kerosene is available almost anywhere in the world.
A lot of backpackers like alcohol stoves. It can be an expensive stove or a free home-made one. Fuel readily available. Provides less heat per volume than other fuels so don't get a stove that is too small for what you cook.
It is possible to run an inductive cook tops with solar in a camper.
Charcoal is harmful to use indoors, don't consider using one.
Wood burning stoves will be problematic in burning ban areas. Finding wood can be easy or hard or impossible. Collecting wood in some treeless areas is unlawful.
Solar stoves depend on having sun. Great in Arizona, not so good on the Oregon coast.
I have used liquid white gas stoves for over 60 years without problem or accident. A white gas stove would be my recommendation. I can't be more specific without knowing your use.
-- Spiff