The following is my personal experience & opinion:
As a fellow New Yorker, I think NYC weather in August is more tolerable than say Hong Kong, Shanghai or any where in southern China. I've lived in HK for an extended period and found the weather only tolerable about 3 months (winter) out of the year. In short, the weather in Kunming is simply ideal.
I've been visiting Kunming monthly since December of 2009 and finally relocated here from HK in August 2010. So, I've lived through the 4 seasons in Kunming 1.5+ times. Relative humidity can be as low as 20%, and in general, about 30 to 50%, but you'll hardly notice it. I am a hay fever & eczema sufferer with intense symptoms in NYC. These conditions have not once affected me in Kunming.
My first winter (2009-2010) here was the driest season (no rainfall) in recent Kunming history but the temperatures were, as I recall, in the 40sF to 60sF range. Temperatures can be in the 70sF with the sun in your face but in the 40sF at night. The past winter (2010-2011), I was told by natives, was the coldest winter in the past 15 years. Temperatures were in the 30F to 50sF range during daylight hours. At night it was very cold because there is no central heating in Kunming. It'd prudent to consider owning an electric heater of some sort for the winter months. It even snowed a few times but the ground was too warm for the snow to stick. May & June are supposedly the hottest months of the year, so I've told and it seems to be the case so far. Temperatures vary from the low 70sF to the high 80sF usually with comfortable low humidity. While outdoor temperatures may feel hot due to the intense sun rays because Kunming, like Denver Colorado, is about a mile above sea level. But once indoor (at home) the temperature falls about 10 degrees F so air-conditioning is never needed. A fan is all that may be needed for the summer months.
If you should relocate to Kunming, I strongly suggest that you find an apartment with a southern or south-western exposure. This orientation in the northern hemisphere will allow the sun to warm your apartment during the day on winter months due to the lower sun angle and then slowly release the heat (stored in the typical concrete and masonry residential construction employed in Kunming and China) at night when the temperature drops. In summer months, due to the earth's rotational change to a higher angle, sunlight will hardly pierce into the apartment to contribute any unwanted BTU. This exposure, vs. east or north, also provides the apartment with the most hours of bright daylight throughout the year.
Since you are American & have lived in Japan for awhile, some starter non- climate related details for your consideration before making the big move are (not in any order of importance):
1. Language (Best if you can speak some Mandarin Chinese)
2. Food (Kunming food is usually oily, salty, and spicy hot)
3. Western grocery availability (Limited choices & quality)
4. Healthcare considerations (Below par with western standards)
5. Cultural differences/practices (i.e., personal & public hygiene)
6. Work / Visa considerations & potential difficulties