The closest production bike available in the US similar to omafiets would be the beach cruiser. They're available as a single-speed with/without coaster brakes, or internally geared, have wide handle bars, step-through or stylish but still easy mounting frame, and often have color-matched basket and rack options.
Careful with what you wish for. Omafiets and cruisers work where there aren't significant hills. Heavy single speeds really suck when you're faces with even a moderate 4% grade. Practical urban bikes in the US really need some gearing.