Finally transiting from LRK to PST....

I'm a 1K who does *A RTW in F(A) 2-3 times a year. I am thinking of interpolating a side trip on SQ from SIN to PVG or PEK into the following itinerary (mostly on SQ or LH)
FRA-ORD-LAX-NRT-SIN-BOM-FRA.
I would arrive in PVG or PEK (out of SIN) in the afternoon, and have to leave the next morning to make my connection in SIN for BOM. Some questions:

• Clearly there would be problems seeing any sights -- but has anyone else experienced seeing either city for an evening, and enjoyed it?
• If so, which city would you choose?
• Can anyone suggest a particular guide that you'd recommend?

If neither city is worth it, my fallback position is to either spend the night in SIN (haven't done that since before I was married!), or change the itinerary to LAX-AKL-SIN-BOM, which would mean UA (over NZ) for the sleeper seat (but no caviar or Krug!)

Thanks in advance for the help