Greater ceiling height is always desirable for resonance, but be careful with this. As mentioned above, it's best that the ceiling height not be the same as the length of one of the walls, or that length divided or multiplied by 2 or a multiple of 2. For example, if one wall is 16 feet long, the ceiling should not be 8, 12, or 16 feet high. If your ceiling is more than one-and-one-third times the length of the shortest wall, you may have a problem of reflected soundwaves that will require some dedicated acoustical treatments, though not necessarily. I've worked in some rooms with very high ceilings that sounded fabulous, mainly because the extra headroom helped the low notes sound more full and deep. It all depends on how "live" (resonant) the space is, and exactly which room surfaces are reflecting the sounds of the piano. If you have a sloped ceiling, the best results will likely be achieved by placing a vertical piano against the wall where the ceiling is lowest, or a grand piano facing out from the same wall and into the area where the ceiling is highest.
Where to Place the Piano in the Room
[Note: Moving a piano can be dangerous. Have professional movers present to avoid injury to persons or damage to the piano and floors.]
Try not to push the tail of a grand, or the end of a vertical, all the way into a corner of the room. While doing so might give the lowest octave more power (low frequencies are boosted by adjacent wall and floor surfaces), pitch clarity and tonal evenness will suffer. The hard sound reflections coming off both corner walls can also kick back into the player's ears a lot of high-frequency "hash." Vertical pianos are best placed against a room's short wall, with the center of the piano one-fifth or one-third of that wall's length from the nearest corner. Try the instrument in both locations, listening for evenness of tone across the scale. Then slowly move it, a few inches at a time, in either direction to fine-tune the sound for clarity.
Finding the right spot in the room for a grand piano involves some effort but is not difficult. Begin with the piano near a corner of the room; if possible, position it with the long side across the corner at a 45° angle to the walls, with the open lid facing out into the room toward the diagonally opposite corner. This will keep both ends of the piano equidistant to the walls and corner behind the instrument, enhancing evenness of tone throughout the piano's frequency range.
Now, measure the distance between the corner behind the piano and the diagonally opposite corner. Then, keeping the piano at a 45° angle, move the piano one-fifth of that distance out from the corner, in the same direction you just measured. Open the lid and play scales through the instrument's entire range, listening for even tonal quality and clarity of pitch. Then move the piano farther in the same direction, until it's now one-third of the way out from the corner. Play it again. Then, placing the piano in the best-sounding location of the two, slide it, in very small increments, back toward the wall closest to the keyboard end of the piano, maintaining the 45° angle, and playing the same scales after every change in position. Then, once you find the "sweet spot," begin slowly rotating the piano by moving the keyboard end very slightly, a few inches at a time, in either direction, playing the same scales every time. This procedure can take some time, but it's well worth the effort, and not as difficult as it sounds. You'll probably be amazed at how big a difference very small changes in position can make in the way your piano interacts with the room boundaries. While this may not solve all of your room problems, I have yet to find a situation where it didn't significantly help.