This time of year, I'd say your best bet is the southern Sierra (until it gets too cold or we get our first real snow). Golden Trout Wilderness, as others have mentioned has some nice areas (and dogs are welcome). You can enter from the west side off Hwy 190 behind Porterville/Springville or from the east side around Olancha.
I wouldn't expect much water on the west side of the Golden Trout right now except for the main rivers (Kern/Little Kern) and some of the larger named creeks. I'd assume most smaller tributaries and springs are dried out.
Lots of areas in the 6,000'- 7,000' elevation range that should be fairly mild (not too hot during the day, not too cold at night).
Beware of coyotes as others said. You're also in rattlesnake territory still at the lower elevations in the Golden Trout, particularly on the west side.
Other options closer to home…
Mt. Pinos area of Chumash Wilderness in Los Padres NF.
Reyes Creek/Beartrap Creek area of Sespe Wilderness in Los Padres NF.
In a typical year, both of these locations would have (some) water. This year is not very typical and water may not be easily available. Fires are outlawed throughout LPNF at the moment. Both of these areas are in the 5,000'+ elevation range where snakes, poison oak, etc. (while still present) become less common.