Living here, I don't have much need of a long-term parking location, so I'm not sure. I looked up Park-and-ride lots, and this one
here is the only one I would leave my car for any number of days. You would then need a taxi or Uber ride to get to Greyhound. There are zero shown in Visalia.
If I were doing that trip, I think I would drive to Sequoia, and park in a trailhead parking lot or the
big area near the Lodgepole campground (ask rangers first). I think cars would be far less apt to be vandalized there. Then on your return trip, take the shuttle into the park and get your car.
Another option would be in front of my house, but you would need to leave the keys with me so I could move it around.
And yet another option: Take public transportation (i.e. Amtrak) up to Visalia.