Question: Given an Earth-like planet, what sort of geological features or weather systems are required for a place to have the same average day and night temperatures throughout the whole year? Is such a thing even possible?

The closest I could think of were tropical climates that are hot all year long (though even these have cooler wet seasons), but I'm looking for something more temperate, around 15-25°C during the day.

The minimum area of the region should be roughly as big as Belgium.

Answer: 
The reason of why we have seasons, and those are always opposed in the North and South hemispheres, is because the axial tilt in the Earth rotation axis, which is 23.4°. This gives a huge difference of the Sun's light incidence over the planet between the Summer and Winter seasons.

Let's calculate the higher and lower effective Sun's light incidence over various regions of the Earth using a simple formula: **c = cos(incidence angle)**

In the regions near the 0° latitude (the Equator) the difference is from 100% Sun's light incidence at the equinoxes and 92% at the solstices (both twice a year) which gives the tropical regions barely the same temperature every day.

At higher latitudes (let's say Rome, at 41° 54′ N) the differences can be from 95% at Summer solstice to 42% at Winter solstice, which makes a hot Summer and a cold Winter.

If you want a region to have the same temperatures every day a year, your world should have its rotation axis perfectly perpendicular to its orbit (0° axial tilt). This way the temperature in a certain region will depend only on its latitude since you will no longer have seasons.
This may not be the answer you are looking for, but thought I'd post it anyway: if a country is close to the equator (e.g. Sri Lanka), the temperature would be same (approx. 30 degrees C) all year around. The day time is also fairly constant i.e. sun rises at about 6am and sets at about 6pm (variation through the year may be about 1 hour).