Well, since you're out there, I'll assume for you, home is FAT. I'd do what I could to get back there.
As others have said, fly the plane first.
Then, second, fly the plane.
Third, fly the plane.
Then, pull out the sticky note you have handy, cover the failed instrument, so you don't read false readings on accident. You do keep sticky notes with your, right?
Out in the valley there, I'm assuming tule fog, so not all that cold, so no worries about icing.
When you are ready to talk, and have the plane in control, inform ATC of the situation, and the request to climb into VMC to verify vac inst are good since you seem to feel the need. Also, have them verify the reading they show for your altitude.
Personally, at that height, I'd do "turn coordinator inop, request lower if possible." You know it is all valley out there, they give a heading, and alt to go to, and you are back VFR below the stuff, since you are only a few seconds from it. Non-mountainous areas are only 1000' of clearance, and you should have that by the time you get down into VFR. If they won't give that, then go for the "request higher to confirm systems in VFR conditions" mentioned above. That's just me, because I know there is nothin' out in the valley there. Situational awareness though. If you don't know where you are, get VFR if you can, and find where you are on VFR and IFR charts. Review the approach you want, and go from there. The guys in the FAT tower are great to work with. Second only to maybe the SJC tower folks in my experience.
So was this a real situation, or just a, 'what if'. If real, let us all know what you did. If not, let us know what you would have done had it been real for you.
Josh