I'm surprised that neither of the current answers makes reference to what exactly the Pinyin phonetically transcribes.
The name of the city, romanised in Pinyin as kun1ming2, is pronounced [ku̯ən˥ miŋ˧˥]. As hippietrail correctly notes, there is a semi-vowel in medial position in the onset.
hippietrail's transcription of 'kweeming' reflects the semi-vowel in the onset, plus the assimilation of the [n] in the first syllable to the following [m].
The reason for the confusion is that Pinyin rimes aren't meant to correspond directly to English orthography. This is why a Pinyin syllable like yuan is mispronounced by virtually every English speaker, where a correct transcription might be [yɛn].
In particular, there's a quirk of Pinyin regarding syllables with the nucleus [u̯ə]. In Pinyin, this diphthong is transcribed
sun etc) except when the initial is zero, when it's transcribed
wen. This quirk of Pinyin may be responsible for your question — perhaps its pronunciation would be less surprising if Kunming was instead transcribed
Kwenming, as would be the case if this quirk didn't exist!
To sum up, you've encountered one of the quirks which make it hard for a naive English speaker to approximate Mandarin based on the Pinyin; although Pinyin uses Roman letters, the values diverge considerably.