Hopefully something silly I'm overlooking. I started building my map with this sample code
But once I started using my own data, it isn't appearing correctly on the map. Example: These coordinates [38.90309, -77.05070999] in Washington DC show up somewhere in Antartica, as do the other US coordinates.
Your coordinates are incorrect.
Correct answer is
view.center = [-77.05070999, 38.90309];
You probably just have the values reversed. When dealing with a point, ESRI expects the longitude(x) to be first, and latitude(y) to be second.