I am thinking about using the 144hr visa free stay in Shanghai on my way back from Osaka to Berlin in May.
While I am very eager to explore Shanghai (first time to mainland China), I was wondering if I should stay all possible 6 nights in Shanghai. And do a day trip of two to any possible sightseeing spots in Jiangsu or Zhejiang provinces. Or if there is a destination in either province which would call for an overnight stay.
My preference would be to stay in Shanghai, as my return trip to Europe will depart in the AM hours. And going elsewhere would require at least a last night in Shanghai again. So technically, I would need to move twice if I wanted to spend a night or two elsewhere.
Any opinions on this?

It depends on "how far" you wish to go in these two provinces but all key cities are easily done as a day trip from Shanghai. I would seriously consider this option as it avoids having to carry luggage and checking in and out of hotels.

There are many destinations in Jiangsu and Zhejiang well worth more than hours on the road or rail for a quick visit, and worth staying overnight for a night or two, sometimes to use as bases for day trips from there.

You can always leave most of your luggage at your initial hotel, and return there for one night, taking a day pack or lighter bag with you.

I'd recommend Shaoxing for a mid-scale city with a completely different atmosphere to Shanghai, a lot to see in the town itself, and the base for an interesting day trip to Anchang and other rural sights.

I basically agree with what CanadaChinaTraveller said, but the night of Xi Hu(West Lake), the best known lake in China is worth a visit. It takes an hour from Shanghai to Hangzhou if you take the high-speed rail, the last train leaving for Shanghai is 21:21, and you can still make the last metro.

Thank you all for your valuable input.
I must admit that I had not thought about the option to leave the bigger bag in Shanghai and just take a smaller backpack for an overnight stay elsewhere.

By the way - I don't see this one week in SE China as a once-in-a-lifetime opportunity. Return flights from Europe to China are usually cheap. So far, I had just been too lazy to go through the normal visa procedure - and too cheap to pay €130 for a visa.

I don't find daytripping from Shanghai very satisfying, unless it's just to one place for one day. To keep running up and down the rails and the roads back to Shanghai gets old really quickly, even with the high speed trains. Shanghai is also the most expensive hotel city on the mainland.

OP, if you're going to use the at least 4 days of that 144-hours (6 day) allowance, I'd suggest you plan 2 nights elsewhere then Shanghai at the end. For instance, if classical gardens are an interest, fly into Shanghai then get immediately to Suzhou and spend a couple of nights there. One day to explore gardens and other locations of interest, another part day to visit nearby Tongli water town. Then high speed to Shanghai and finish up there. Other similar combinations possible with Nanjing or Hangzhou.

Thanks for your input.
That would indeed be a solution to move the x nights in Shanghai to the end of the trip. So far, we have planned to use the full 6 nights of the allowance.