First, make sure your garage uses 24VDC. A more common control voltage in residential wiring is 24VAC, seen in doorbells and thermostats. AC voltage is a big mess for a DC device, but it works with transformers!
Since it's part of a building, it must reasonably comply with the electrical codes. Fortunately those codes are pretty easy on low voltage (30V) low power (<55W) devices. You will need to use proper enclosures and do wiring to the low standards of doorbell or thermostat wiring (e.g. Neat and workmanlike, don't be stupid, make an effort to staple it out of harm's way, and don't use mains power wiring as a hanger.) So in a Code context:
A DC-DC converter
is a great way to handle it. The converter will make less than a watt of residual heat, and will be small, so it will fit neatly into a common, cheap steel 4" or 120mm square junction box. The steel's thermal conductivity and the size of the box will take care of heat dissipation. Its current draw will certainly be within the range available from the opener.
Code requires the use of "approved" equipment which generally means it is UL listed. "Equipment means "not components": difference being, the equipment has labeling/instructions describing its consumer use, and UL tested and listed it that way. But again, rules are relaxed for low voltage <55W stuff. The point of this is, favor a DC-DC that is packaged more like a finished good, i.e. That has screw terminals and a case, rather than wires sloppily soldered onto a unit meant for PCB mounting. If it's packaged neatly enough, you may not even need a steel junction box to hide it.
I've worked with resistor laddes a fair bit. For instance, Westinghouse HL traction drive equipment (the L is for line powered, not battery) uses a resistor ladder to synthesize roughly 80V from 600V line voltage. The lower resistor, between load and GND, keeps the voltage from floating upward toward 600V if there is no current draw by the load.
But the voltage varies considerably, since the lower resistor is paralleled with between 0 and 15 contactors on a 5-car train. This varying of voltage is the Achilles' heel of resistor ladders. You mitigate it by making the upper and lower bypass resistors larger (in watts and physical size, smaller in ohms). For any reasonable working range, the vast majority of power will be consumed in the resistor ladder, not the load.
In your application, you need to spec your resistor ladder so your voltage stays between 3.3V and 5V at load draws between 0A and 250ma (or whatever measurement proves out). The math isn't overly complicated, but that's a narrow range that I expect will require a fairly enormous resistor ladder. So you're going to be making a lot of heat, and will need appropriate safety caging for the resistor bank. I fully expect this will exceed the supply capacity of the garage door opener's power supply. It may even exceed the 55W statutory limit for relaxed rules for low voltage wiring! All in all, ladders are just not for things with narrow voltage requirements.
A linear voltage regulator
Something like a 7805 regulator is a resistor ladder -- but with the lower balance resistor deleted, only the Arduino as the lower resistor, and the regulator as a "smart" upper resistor, changing its resistance on the fly to track the load current. The whole circuit flows whatever the Arduino draws, which is up to 250ma, you say.
The voltage regulator must dissipate the difference between supply voltage and lutput voltage, e.g. 19-20.7 volts x circuit current. E.g. At 250ma that'd be about 5 watts. That will need to be heatsinked appropriately. Too much to use a 4x4 steel box as an ad-hoc heatsink.
Almost all voltage regulators are made for external heatsinking, so you have a big packaging problem as far as making it look like "not a science project". And you have to deal with ultimate heat removal: the heat sink has to interchange with ambient air, and you can't just let the junction box get hot.
Expand mains power at the opener; add a "wall wart"
A few garage door openers have provisions for a receptacle (mains socket e.g. NEMA 5-15). If not the socket, a pre-cut knockout where a socket could be installed. You could retrofit that.
Or you could fit a duplex mains socket at the garage door opener's supply, give it a power cord, and now you have an open socket.
Plug a wall-wart in there and done.