i feel there should be an area in the mountains, to either get geodes, new or old ores, or a new crop specific for the mountains or just something new in a newer area.
I feel like the geodes and ores part might be better served by making the quarry less of a disappointment, but I definitely agree that it should be possible to really go into the mountains... even if it's just climbing A mountain to pick a midwinter quest item as I remember it being in Harvest Moon for SNES.
Similar to the beach, the usefulness of the area is kinda...lacking. At least in the forest you can cut trees, go to the secret forest, visit the wizard and gypsy, etc. A quest in the mountains or out at sea would be really rad.