How far off the 395? Past Kramer junction, turn right at Red Mountain and head over to the Pinnacles. On the way there is an off road area (cant remember the name) Panamint Valley is a short distance from Pinnacles. Back on 395 heading north, your going to be skirting Death Valley. Getting into Lone Pine you have Alabama Hills to the left and Death valley to the right. If you like old school music the "Joshua Tree" album by U2, the tree itself is 20 odd minuets toward the east from lone pine. As mentioned different things though Bishop. Continue up to Mono Lake. On the back side is the remains of the Mono Lake rail road that went from there to Bodi as well as the Tufa (spelling?). North side of Mono, north shore, are the Fissures. Kind of a cool hike. There may or may not still be the town they made for one of the old Eastwood westerns there (Pale rider?) right on the waters edge. Back on 395 to Bodi ghost town. Trivia... almost all the bad guys from the show Bonanza came out of Bodi. Then the town of bridge port. Bakery in town, get the Haystacks....yum.
I know there's more but that's what came to mind while i'm screwing off at work right now.
Forgot to add, not alot of "off-roading" along 395 until you get close to Tahoe. Mostly dirt access tourist stuff and cool history