Pianos respond the best to a stable environment. The more unstable the environment, the more unstable the piano will be.
If the piano is located by a door that is used a lot, the blast of cold air that hits it every time the door opens during winter will affect the tuning stability. The same is true if the piano is located in the path a heat or A/C vent. The cycling of heating or A/C will keep the environment unstable for a piano. The same is also true for a piano next to a poorly insulated outside wall or window.
Direct sunlight can also affect the finish on the piano as well as cause discoloration on the white key tops.
Heaters, heat vents, and fireplaces are the enemy of the piano. Moisture content is the life blood of wood. Over time, the dissipation of moisture in wood causes it to shrink and weaken, causing cracks, loss of tone, glue-joint failure, and broken parts. Excessive dryness will speed up this process.
If your piano is in a dry area and cannot be moved, consider using a humidifier for the room during dry winter months. Pianos like 40-45% relative humidity - just like people do.
Pianos in houses near the water, or in damp basements, can be susceptible to excessive moisture. Moisture can tarnish or rust strings and other metal parts and cause mold or mildew to grow on felt parts. String breakage can result in extreme cases. In cases where excessive moisture is a problem, dehumidification should be used. Air conditioning is great for this purpose and feels good, too, in humid summer weather. If A/C is not an option, a good dehumidifier will do the trick.
The ideal location for your piano is by an inside wall, away from doors to the outside, away from heaters and air conditioning, and not in rooms with actively used fireplaces.
Older pianos sometimes have issues with tuning stability, especially if they have been located near a heater for many years.