I had an idea where the modern US is ISOTed to the old world, So I did a thing where I transposed 2000 municipalities from the lower 48 states onto positions in the Old World:
https://drive.google.com/open?id=1kf1XnTZVUjwcpT7S6xIoQv_8944&usp=sharing
The map is searchable. Latitudes are exactly the same for all cities, but longitude is... funny. I tried to (1) preserve relative longitudes so that a city to the east would stay to the east and vice-versa, and (2) position cities so that they ended up in a place that's survivable and not in the middle of a desert or ocean. To that end I used a spreadsheet with the latitudes and longitudes of both old world cities and new world cities and did a bit of matching. However, my goals began to contradict each other and I ended up with some weird results, like some cities in Maryland being west of some cities in Iowa. Even so, the east coast is on the east coast and the west coast is on the west coast, and cities on water are not too far from land.
If I had to pick transposition areas for Alaska and Hawaii, I'd probably go with Scandinavia and the Caribbean, respectively. The Caribbean isn't in the old world, but then again Hawaii isn't in North America.
As an example, here is where my home city of Cleveland ended up, on the Macedonia-Bulgaria border:
View attachment 315927
The city on the upper right is Burbank, Illinois, which is decidedly not northeast of where I am.