Hello and welcome to the RTA forums !
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September into October is a fantastic time to travel, along with the blue skies and Fall colours you have less heat and fewer crowds to contend with.
You should know that the 'Skywalk' is on Indian lands and not part of the National park system. It is more expensive and difficult to get to than the NP as the road is in poor condition and you will need to get a tour bus to avoid breaking your car rental agreement. [no unpaved roads] It will not offer the same views made famous around the world through photography and film either. I would recommend the National park, although it is your choice, those are the facts to ponder.
If you decide to head to the National park, it may be wise to book your lodgings there as well, although you will find cheaper lodging outside of the park in Williams or Flagstaff.
Tahoe is an option, but another I would consider is to go to Zion NP, and possibly Bryce canyon in Southern Utah. That would be from SF to Yosemite to Death valley to Vegas to Zion[Bryce] to Grand canyon [?] to San Diego to LA to SF. A lot will depend on at what pace you are comfortable with and how long you wish to spend in each place.
Look around and when you have some ideas together we can help piece it all together.
Note I have deleted your other thread as it is not needed. Any further questions regarding this trip, pleas keep in this one thread. Thanks !