I have found DV to be very difficult for backpacking. Your time of year is correct but it still can get warm up to low 80's. It's a lot of water to carry. I would consider going to a good basecamp location and do day hikes from there or if you really want to pack, do individual overnights with enough water for another day. In other words, one day out means two days of water carried.
In terms of where to go, well there is 3.4 million acres to explore. I like the vicinity of the Inyo Mountains, Saline Valley, and Panamint Dunes. I saw chuckwalla lizards there that matched the color of the nearby rock. Couldn't see them until you were really close. Picked them up without complaint.
You will be limited by the type of vehicle you have and it's condition. Do not go alone.