How Soon Is Now - The Smiths
Whisper To A Scream - Icicle Works
New Gold Dream ('81 '82 '83 '84)- Simple Minds
I Want You Back - Hoodoo Gurus
Secret - OMD
Heaven - Psychedelic Furs
Someone's Calling - Modern English
Under The Milky Way - The Church
Ceremony - New Order
Wishful Thinking - China Crisis
I guess technically, some of these bands are considered more alternative than new wave, but considering that when new wave hit the air here in the US, it was a bit more of a general term than specific. Pretty much anything that wasn't Top 40 or metal was seemed to be considered New Wave.
I do need to add as an introduction that I am of the fortunate generation in the New Wave era. I was a senior in high school when MTV first came to be and I remember well watching when The Buggles video was aired the first time. When New Wave was at it's peak, I was in college.
I was born and raised and now live in the Salt Lake suburbs, so a shout out to any others here.

New Wave or nothing!