Yes, avoid the following:
Never Near Heat
Do not display your stone sculpture over, under, or in close proximity to a heat vent. The added heat will dry out the stone, making it more brittle. Stone sculpture should last 500 years or more.
Never in Direct Sun
There is not a good Ultraviolet (UV) protective sealer for stone. The sun will surely fade the color of many types of colorful stone very quickly. Do not place your colorful stone sculpture in direct sunlight or under artificial lights that emit UV (such as fluorescents or CFLs).
A wooden base should never be placed in the sun as it will deteriorate rapidly and significantly. Protect your investment, and do not place your sculpture in direct sunlight.
Never Near Moisture
Many sculpture stones will absorb moisture even inside. In drier climates, like my home in Colorado, this may not be a problem. But in damper climates, stones will absorb moisture and this can result in deterioration. White marbles, in particular, with exposure to moisture can develop a biofilm. All my stone sculptures are sealed against oil and moisture for indoor display. Stone sculptures not sealed specifically for outdoor display should be displayed only indoors.