Late September can be good - cooler temps (especially night temps), less crowds, and low chance of bad weather. However, as mentioned, the water flow will be minimal to nonexistant - especially this year as there was no snow last winter. Unfortunately, fires are a big potential. So keep watch for any fire reports for the next couple months.
Early September is likely to still be hot and the crowds bigger. Lack of flowing water and fires will be the main letdown.
Fires in the region will also affect visibilty of the night skies.
As mentioned, spring gives you the biggest bang for flowing water - especially if there is snow this winter. Minimal concern about fires, but fire damage from this year may affect campgrounds next spring. What time in spring will depend on snowfall. If minimal snowfall, then roads will open sooner. If lots of snowfall, then roads may stay closed later. Spring will also see wildflowers in the meadows. Night skies will be clearer with no fires.
If you aren't interested in doing a longer trip and seeing more of California, I would stay on the east side. From there, you can also visit Mono Lake and Bodie Ghost Town.