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 un
(kun
, 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.