Shanghai, Hangzhou and Suzhou
The Yangtze delta: 25-minute hops, real commuter rail, and why two-day visits work.
The delta is the densest cluster of useful rail in the country: Shanghai to Suzhou takes 25 minutes, to Hangzhou under an hour, and all three cities sit on one frequency diagram that goes until late evening. You can base in Shanghai and day-trip everything, or move cities and never lose more than a morning.
The mistake visitors make here is treating it as one city. Hangzhou is a lake surrounded by tea hills, Suzhou is gardens and canals, Shanghai is neither. How many nights you spend where is the whole question.

Shanghai In Three Days: Arriving, Sleeping Right, And Spending Well
Stay on the Puxi side, ride the metro not the maglev, and treat Pudong as a visit rather than a base.

Hangzhou: West Lake, Tea Hills, And The Easiest Day Trip From Shanghai
Free lake, paid boats, tea hills in the afternoon; two days, or one very good one.

Suzhou: The Gardens, The Canals And Two Days That Work
Three gardens, one museum, and the lanes between them on foot.

2 Days in Shanghai: Old City West, Skyline East
Fight the temptation to cross the river twice. Puxi in one piece, Pudong in another.

2 Days in Hangzhou: The Lake On Foot, The Temple At Dawn
Circle the lake on day one, climb into the tea hills on day two.

2 Days in Suzhou: Three Gardens, One Canal Street
Two gardens before nine, a third after dark, and the canal streets in between.

Shanghai To Hangzhou: A Day Trip That Genuinely Works
Take an 08:00 train from Hongqiao, and book the return while you are still at breakfast.

Shanghai To Suzhou: 25 Minutes, Two Stations, One Wrong Choice
Book to Suzhou station, not Suzhou North, and start with the Humble Administrator’s Garden.

Hangzhou To Suzhou: Which Train To Take And Where To Get Off
Fast train to Suzhou, then twenty minutes on Line 4 into the old town.