My adsb coverage is not very good here at home and I am thinking about moving it up to KSJS which is up on top of the mountain 700 ft + higher. My concern is will I still be able to see it on my home computer.
That will depend on what your arrangement is for network connectivity at the other site. Will you have remote access to the network you are going to connect it to? Will they allow you to set up a VPN or SSH tunnel to your box?
What else is up on the mountain?
If there are cell towers or other transmitting equipment up there on a similar frequency, the receiver might need signal filters to prevent it getting swamped by the other stuff.
Take the Pi up the hill with the little mag-mount antenna and a USN cigarette lighter charger and see what sort map you get out of dump1090 (on a laptop, etc)