North road bars look like this:


I find them to be really comfortable, partly due to the swept-back grips, which place the hands in a more natural position than conventional flat bars. They work with flat-bar brake and shift levers, though I'd use thumb shifters or grip shifters rather than brifters or triggers.

Alternatively, I'd consider an older road bike, which tend to be built more for transportation than racing. Set the handlebars at a sensible height, and use all of the available grip positions, and you'll probably find drop bars to be quite comfortable to use.