The following screenshots illustrate what building slots open up for each of the 11 mountains that are removable. Since there are only 8 mountain buffs available and 11 mountains, review the screenshots, take your time & choose wisely. Shots were taken on my test island and on my lovely Calliope_Jeyne's test island. We concentrated on the mountains with a few of the larger rocks and/or rocks close to mountains included. Hope this helps with your planning while saving you some grief and a few gems. Marked all building spots with wheat fields.
Started in Sector 7 at the north west corner of the island and worked clockwise from there.
Sector 7
Removed one large rock, gained 2 building spots.
Removed a combination of rocks and rubble, 4 in total. Yielded 4 building slots.
Removed 2 mountains, 1 rock, gained 4 building spots. Could probably fit an improved storehouse and 3 regular buildings here.
Sector 8 / border of Sector 7
Removed mountain in sector 8, gained 2 spots.
Removed large rock, gained 3 spots.
Removed another large rock, gained enough room for an improved storehouse and 1 other spot.
Note: When I removed this rock on my home island, did not gain enough room for an improved storehouse and 1 slot because I had 4 (2x2) buildings clustered where the watermills are. I moved one of the buildings to get the fit shown above since I'd just paid gems for the storehouse.
Removed 1 rubble on either side of storehouse (2 total). Each yielded 1 spot.
Sector 7 close to sector 4 - Removed 3 rocks, gained 1 spot per each rock removed.
Sector 9 ~ North
Removed 1st mountain on left. Gained 2 spots.
Removed next mountain, gained 2 more.
Removed 3rd mountain, picked up 1 more spot.
Removed 4th and last mountain here, picked up 2 building slots.
Removed large rock, gained 3 slots.
Sector 9&S6 border
On the right removed 4 mountains and 1 rock. Picked up 12 building spots. To the left, removed 2 large rocks. Each rock yielded 2 spots.
Alternate on S9&S6 border
This alternate shot of the same area was taken on my home island. Removed only 3 mountains and 1 rock. Picked up 10 spots and promptly filled them with nobles.
Sector 6
Removed 2 large rocks, gained 3 spots