There have been a number of ergonomic improvements and considerations to road bikes in the past ten years. You should be able to ride comfortably in the drops and on the hoods.

Shorter top tubes, or 'Womens Design' on the frame allows a better fit for many. Short reach handlebars put the shifters more comfortably into your hands.

Threadless steerers allow bar height adjustment as well as stems with a rise angle. All of these things bring the bike and the controls to you, rather than you reaching for them.

Finding a bike shop willing to work with you, size you properly and allow test rides is a first step. Any number of brands will be good candidates.