Im a nomad/tourist/student in the Kunming/Lijiang area for the past 8 months! I'll see what I can help a bit here!

here's a recap of what you typed earlier:
Day 1 : arrive Kunming at 3pm to begin Kunming travel. Walk around Kunming town.
Day 2 : morning flight to Diqing (Shangri La). Arrive at 9am. Walk around and spend 1 night.
Day 3 : after lunch, afternoon overland (?) transfer to Lijiang. (Anything to see enroute?) Walk around Lijiang town.
Day 4 : Snow Mountain/Black Dragon Pool
Day 5 : cycling around outlying villages
Day 6 : morning flight back from Lijiang to Kunming.

I think your Day 1 is a bit constrained, but with your time, you can hang around downtown, enjoy some modest spring city weather. There is a temple called "yuantongsi" temple an old buddhist temple closes at 5-6ish. But since your day is limited here and Day 6, there's not much to see but enjoy the flowers. DO NOT GO TO BIRD AND FLOWER STREET. it has no birds. Shilin Stone Forest is one of the attractions of outer Kunming, pricey but a one-time 70% day go is all that's needed. inner Kunming has flowers... esp Cuihu Green Lake.
Shangri-La (must-see for top 10 China tours) is gorgeous.
Lijiang is amazing! I will help you modify a bit on the Lijiang side...
Jade Dragon Yulong Snow Mountain and Blue Moon Lake (Lanyuehu) are near each other, should be good and sunny in April, save that for 70% to a whole day. Ride a yak too! (FYI don't waste money enroute to Jade Dragon on O2 bottles(80rmb) or a big winter jacket rental (40rmb) on ground kiosks if you don't need it. On site, on top of the mountain and a kiosk just before ascent, there sells it for much cheaper (60rmb, 30rmb respectively)
Lijiang Dayan old town, elephant mountain and black dragon pool are closer to each other than the Snow Mountain, so that would save you some time and physical energy. There's a neat Naxi museum near the black dragon pool, among other sites to visit and crawl. You may also like to visit Shuhe Old Town, Shuhe Ancient Town is much quieter than Lijiang old town, so you can hear the peaceful horseclops and river flowing adrift, with a daily dance in the theatre at 730pm (only if it's a good night). BIG but playful dogs happily stroll these streets. (Can you tell which one I like better :P) Located west of the highly anticipated and gorgeous ACCOR GROUP Pullman Resort and Spa [(answers your original #3 question!) (They're open April 1st, so check for their opening promotion ~ i think it's 3 nights, 1 free..)]
Day 5 is further exploration, or you can spend approx 50~80RMB (from Lijiang) to go up to Tiger Leaping Gorge, HIGHLY RECOMMENDED to visit from many many foreigners, friends and myself! Go early, or spend the night there too. (It is approximately enroute from Shangri-La to Lijiang, so plan accordingly, if interested.)

Contact me if you'd like. I try to help people here and everywhere.

Cheers on your trip! Make a Story out of Everyday. Share life.

Andrew Ames AKA Darwin
Canadian.

Location: Lijiang

More: China tour deals and travel China guide