The diode may be a good choice if your load current and input voltage are fairly stable and known.
Keep in mind that the nominal 0.7V or so drop from the diode will be less at very low current and you'll pretty much get the full input voltage with a very light load. If whatever your load is goes into a sleep mode and the current drops to about zero then you'll see that voltage increase to maybe 3.9V.
If that is within specs, then you are okay, but then maybe you don't need the diode at all.
There are various regulators. The
LP5912-3.3DRVT is one. It can output 500mA with only 0.25V drop (typically less than 50mV at 200mA) and typically draws only about 30uA for its own purposes. It can handle up to 5.5V input.
If you choose to use an LDO regulator, be sure to
carefully read the section on capacitors and follow it to the letter. In this case, 1uF ceramic capacitors are suitable on both input and output.