Ignacio told me that in Spain lots of people have butane cylinders and cook with that. I've read it's quite common all around the world outside of the US, particularly in poorer countries where they don't have gas lines.
"Butane" and "Propane" are both not actually butane and propane. What's called "butane" in most of the world is a mix of butane & propane, what's called "propane" in the US is another mix. The more correct generic name for both is LPG for "liquified petroleum gas" , but the colloquialism is just to say "butane" in the rest of the world and "propane" in the US. The exact mix depends on the temperature - hotter places sell you more butane in your LPG mix.
You can get little single burner LPG ranges for $10.
Propane is totally safe to use indoors. There are a few things to be careful about though.
Propane needs a lot of O2 to burn fully. If it burns with enough O2 it produces only H2O and CO2. That's good. If it doesn't get enough O2, it produces CO. That's bad. Make sure you open a window in the kitchen. It wouldn't hurt to buy a CO detector too, they cost like $30.
Propane is heavier than air. Natural gas (methane) is lighter than air so even if you have a leak it diffuses and goes up through vents and gets out of the house and you rarely get a dangerous concentration. This is why even if you leave a gas burner turned on and not lit you don't get a huge explosion when you light it. Propane on the other hand will pool up on the floor around the stove. This creates a dangerous explosion hazard. It's generally recommended that you keep the cylinder outdoors so that if it leaks there's less risk.
In the US it's illegal to have a 20 pound cylinder or larger inside your home. Many people in the country in the US have a 100 or 500 outside and get deliveries. You could also keep a 20 outside and run a gas line through your window.
Apparently propane cylinder theft is quite common in the US. WTF, people are such hooligans. Cylinder owners lock them. Personally I'd be more worried about someone fucking with the valve or the line if I had my cylinder outside.
Almost all gas ranges can be set for "LP" (that's LPG, which is propane, recall). It's a slightly different gas/air mix so don't try to use LP on a gas range without setting it to LP.
You can get propane-burning range tops (no oven) that are made for RV's for like $600. These could sit right on top of your counter or your old oven.
I haven't completely found a happy solution that I think would be safe and legal, but this is all sort of interesting.