Due to the free visa and the relatively low price of flights (although not so low if one does not want to fly chinese carrier), I am thinking to go to China end of February - early March. I already had 2 trips there : 5 nights in Xi'an and 5 nights in Shanghai. Every trip I stayed into the city proper. I do not speak a word of Mandarin, I am OK taking public transport.
I was thinking to do something like this, what do you guys think:
Land in Shanghai
3 nights in Shanghai
Train to Hongzhou
3 nights in Hongzhou
Train to Nanjing
4 nights in Nanjing
train to Shanghai
2 nights in Shanghai
Depart back to Europe

Maybe stopping on the way back to Nanjing in Suzhou for 1 night but that start to be a lot of packing/unpacking.
Does that sound OK ? I already have been to Shanghai so the time there would be go on some water town in the outskirt I think + possibly do some museum I did not visited before + walk around as I really enjoyed the city my first visit.
Nanjing seems like a town relatively out the touristic path and a good opportunity to see modern china. I am a bit afraid of the level of English there though ?
I generally like history, temples, nice landscapes but I am a very urban person. So landscape are nice but it needs to be accessible by public transport. Hence Hongzhou who seems gorgeous.

I assume you mean Hangzhou? If so, I think 2 nights is sufficient, and 4 seems a bit too much for Nanjing as well. Given this is your 2nd trip and you haven't been to Beijing / seen the great wall, maybe consider taking 3 nights out of Hangzhou / Nanjing and flying to Beijing instead.

Your itinerary sounds great! I’d recommend sticking to three nights in Hangzhou since the West Lake area is stunning, and you can easily explore it via public transport. Nanjing is indeed a bit off the tourist track, but it’s rich in history definitely check out the Nanjing Massacre Memorial and the Ming Xiaoling Mausoleum. As for English, you might find it limited, but most signs are in both Chinese and English, so you should manage just fine. If you're worried about the language barrier, consider downloading translation apps to help. Skipping Suzhou might be wise to avoid the hassle of constant packing. I had a day tour in China through https://gowithguide.com/China If you’re considering a tour, it’s definitely worth. Enjoy your trip!

Yes it is Hangzhou, sorry for the typo.
No going to Beijing is not on the card, I will go one day and properly, doing it as a side trip there would be a rush. 2 nights in Hangzhou and 2 nights in Fuzhou might be another option.

If you were to structure trip as an open jaw, what are your options for endpoints other than Shanghai (not necessarily limited to mainland China)?

IMO, 12(?) nights in the YRD might be a little too much, in light of the vastness of the country, so I'd definitely be interested in making my way to somewhere differentover the course of the two weeks.

If I want to reduce the cost an open jaw is out of the question. And European carrier fly only out of PVG (I will not take a chinese carrier for the international part). I could take a domestic flight to go back to PVG though. 12 days there seems also a bit much to me but then maybe I can take a bullet train to somewhere not too far (Wuhan ? Xiamen ? )

1. Many European airlines that fly to PVG also fly to HKG (e.g. BA, AF, KL, LH).
-Getting "Europe-Shanghai<open>Hong Kong-Europe" to price in the same ballpark as a Europe-Shanghai round trip might require a bit of finessing because some airlines treat Hong Kong as a distinct region.
2. I'm amazed that KL is the only European airline that flies to Beijing (at least through the winter schedule). They are presumably extracting a price premium for this, so you've already ruled them out?
3. Have you looked into CX (many destinations in Mainland China, if you don't mind connecting in HK twice)? They aren't quite as Chinese as the Mainland carriers.
4. Some of the Chinese airlines that fly out of Beijing have codeshares and/or JVs with AF, KL, BA, LH, etc so it is possible to combine them with an outbound to Shanghai for around the same price as a round trip to Shanghai. Personally, I prefer most of them to most European airlines these days, but they all overfly Russia (at least, for now).
5. TK and several of the Middle Eastern carriers also have more Mainland China coverage than Shanghai.

KL was quite pricey. So is CX. I do not and will not fly TK. As you say an open jaw in PVG, out HKG was very pricey. I found a good deal with the LH group out of BUD to PVG so I will likely push the trigger on this one. The reason I do not want to take Chinese carrier on the international segement is the Russia overflying.
But I am going to look into :
3 nights Shanghai
2 nights Hangzhou
2 nights Nanjing
3 nights Wuhan or Xiamen
Fly back to Shanghai and leave from there

Xiamen is pretty nice. Besides the Xiamen-based attractions such as Gulangyu, you can make a day-trip by boat to the Taiwan-controlled island of Kinmen for some historic sightseeing. I just did this (but spent the night in Kinmen and flew onto Taiwan proper from there). Speaking of which, maybe you can check flights to Europe from Taipei.

His good deal out of BUD is almost surely driven (at least indirectly) by Belt and Road forces that don't impact the Taiwan market so much.

fransknorge You might be able actually be able to bring your fare down even further, or at least get a free flight, if you make the destination somewhere other than Shanghai (i.e. tack on a domestic sector).

I will try this.
I am actually going to Taipei next month anyway (on a completely different trip).

It is possible to take a day trip to Suzhou or Hangzhou from Shanghai.
I went to Suzhou by train and took a sightseeing bus from the train station there.
As for Hangzhou a bus picked us up at the hotel at 7 in the morning and came back at 11 in the evening, that was quite hectic.
This was back in 2010 so things have probably changed, now there is a high speed train to Hangzhou I think.

Shanghai > Hangzhou > Nanjing > Suzhou > Shanghai seems ok. All easily doable by HS train.

If you want something off the beaten path, take a day trip to Yiwu from Hangzhou (30 min by HS Train). You can visit a 1:1 copy of the Forbidden city in Dongyang Film City (Hengdian) and go see the Yiwu International Trade Market (where you can buy tourist magnets from any destination in the world in bulk - this is where they all come from - along with other day-to-day stuff you probably use at home). HS Train from Hangzhou west to Hengdian (45 min). Then you can take the subway to the international trade market. From there take a taxi back to the train station.

Lots of good middle eastern food around the trade market.

Yiwu International Trade Market! First time to see this suggested as an offbeat tourist destination but definitely a good one!

Be aware that if you are not looking for something specific, or know exactly where you are going, it would
probably take 3 days to cover the entire market.

Last time I was there I was taken to a Turkish restaurant in one of the buildings - it was fantastic.
And I was amazed by the waiter being fluent in English, Turkish, Mandarin, Cantonese, and German.