I'm not associated with any of the following. I was actually looking for a RHD drive VW beetle in the US (like the NZ/Aus/UK steering wheel configuration).

I came across a beautiful 1952 MG YB, begging to be restored for NZ $5,000

https://classiccars.com/listings/view/888313/1952-mg-yb-for-sale-in-beverly-hills-california-90210

1965 Ford Mustang for NZ $83,000 (US $60,000). Ready to drive

You should be able to talk them down, since it would not be popular in the US (more of an oddity).

I'd suggest an opening offering of US $30,000, and take US $40,000. (NZ $56,000)

Anyhow, too rich for my blood

https://classiccars.com/listings/view/919209/1965-ford-mustang-for-sale-in-scottsdale-arizona-85251

Lots of circa 1970's and 1980's mini-coopers for sale starting at US $10,000

https://classiccars.com/listings/view/895958/1980-austin-mini-cooper-for-sale-in-monroe-ohio-45050

https://classiccars.com/listings/view/907607/1973-austin-mini-for-sale-in-san-antonio-texas-78240

I'd guess it would cost about $3,000 to ship any of these, more for cars that don't run. Choose a "Roll-on/roll-off (RORO or ro-ro) ship if possible, because it's more likely to arrive in good shape than a freight container.