Yeah, I'd agree with moondog to book a hotel in the Jing'An temple area or the French Concession area.

You are correct in that you will get a 24-hour Transit Without Visa so use the TWOV queue at Immigration. I believe there is nearly a 100% chance that on your routing, you'll need to pick up your bags at Baggage Claim, walk through Customs exit, and then look for ground transportation once out in the main arrivals area. Grab some RMB cash either from ATM or bank counter window if using currency notes. I'd just taxi to your hotel if you want to keep your luggage. If you want to park the main luggage at the airport, Left Luggage is available for a fee, just take your valuables with you. Then you can use public transport as mentioned by moondog above. You'll need to recheck your luggage when you check in the next morning at the airline counter, but on this flight sequence it should be checked all the way to KTM so you won't have to deal with at KMG. However, you normally would not go through Exit Immigration until KMG so expect to deplane there and do that. This is a common routing to get from China to Nepal, so MU certainly should have a procedure/jetway escort at KMG for getting you to and through Immigration quickly and reboarded....and likely you'll have fellow passengers doing the identical to you on PVG-KMG-KTM.