Would a day or two in Mono Lake be a good side trip from an October 5 or so day Yosemite trip? How much time would you recommend in Mono Lake and where would you stay?
I'll add to what has already been said...
Sometime during the first two weeks of October in a typical year, the eastern Sierra aspens light up in spectacular fashion. The timing is a bit different every year (dependent upon the climate, the current weather, and exact location) but the second week of October is often a good bet. (Unless a big, windy storm comes through and blows down all of the leaves a bit early.)
This year may be a bit different since the Sierra (and most of the rest of California) experienced a drought last winter. The northern Sierra got about 50% of normal precipitation and the southern Sierra got only about 20%. I'm not sure what the effect will be on the timing of the aspen leaves, but I suspect that they may change a bit early. (I've been in the Sierra many times already this summer, and the conditions already look like September in many places.)
All of this is my way of saying that if you are in the eastern Sierra in early October you should be alert to aspen conditions and be ready to change your plans to include them.
Mono Lake is a good photographic subject at just about any time of the year, though in very heavy snowfall (extremely unlikely in early October) access could be a problem. If you haven't shot there before and your time is limited, I recommend going to the South Tufa area before first light (say 45-60 minutes before dawn) to shoot the sunrise there.
I find that sunsets at Mono Lake are a bit more problematic - though wonderful when you are in the right place at the right time. Keep in mind that the Mono Basin is east of the very high peaks of the Sierra crest, so the light goes into shadow well before actual sunset, especially along the west shore.
A few comments on other topics that have come up in this thread: In typical conditions the drive to Bodie is nothing difficult at all. The first part is paved and the last three miles are a well graded dirt road - but nothing requiring any sort of special vehicle at all. Regarding October Sierra weather: In my experience early October can bring the most beautiful weather of the year to the Sierra. Typical days are sunny with beautiful warm light and comfortable temperatures; the nights are cold, with high country temperatures getting down into the teens. Snow is possible but less than likely. It is not unusual for a front or two to pass through at this time of the year, but they usually (note the use of the word "usually!") pass relatively quickly, dropping a trace to a few inches of snow that will melt in a few days. But do keep an eye on the forecasts. A couple years ago winter arrived on the second weekend of October with serious snow; Tioga Pass road closed and didn't open again until the following spring.
The park service begins to close things down on Tioga Pass road in late September. Park service campgrounds are closed by October, though forest service campgrounds just outside the park remain available, and some lodges are still open until mid-October, including the Tioga Pass Resort just east of the pass. There is no overnight parking on Tioga Road in the park after about the second weekend of October.
Have a great trip!