The shape of the route
The classic Yunnan line runs north: Kunming, then Dali, then Lijiang, then Shangri-La. Each leg is short enough to travel in a morning, which means you can move every other day without spending the trip in transit. The mistake most people make is trying to do all four in four days — that gives you an afternoon in each and a lot of station time.
A workable five days
Day 1 arrive in Kunming; the Green Lake area and a bowl of crossing-the-bridge noodles are enough for the first evening. Day 2 train to Dali in the morning (about two hours), then the old town and the lake shore in the afternoon. Day 3 Dali in the morning — the Three Pagodas and the Xizhou village — then the afternoon train to Lijiang (about 1.5 to 2 hours). Day 4 Lijiang old town early, then Shuhe or Baisha in the afternoon. Day 5 either Jade Dragon Snow Mountain or the train on to Shangri-La.
Adding two more days
Six days lets you sleep in Shangri-La and see Songzanlin Monastery and the old town properly. Seven lets you add Pudacuo National Park, which is a half day and needs an early start, and still gives you a slow morning in Lijiang at the end.
If you have to cut something, cut Kunming. It is a pleasant city and the transport hub, but the scenery that people come to Yunnan for starts at Dali.
Trains, buses and cars
The Dali–Lijiang and Lijiang–Shangri-La lines are both fast, comfortable and cheap, and the stations are outside the old towns by 15 to 30 minutes. Book a few days ahead in high season; the morning departures sell out first.
A private car makes sense for the lake loop at Dali (the shoreline road is 120 km and public transport is slow), for the villages around Lijiang (Baisha, Shuhe, Yuhu), and for the Snow Mountain, where the cable car ticket and the park shuttle are easier to coordinate with a driver. For pure city-to-city movement, the train is better in every respect.
Where to base yourself
In Dali, the old town is atmospheric but the lake villages are quieter; in Lijiang, the old town is beautiful and noisy at night, while Shuhe, 6 km away, is where people who want to sleep go. In Shangri-La, stay in the old town rather than the new town — it is smaller than it looks and everything worth seeing is within walking distance.