Do some research, and look at a variety of bikes. It's true that many roadsters come set up virtually the same as full-on racing bikes; fast-twitch frame geometry, short chainstays, steep head angles... All that.
But not all. You can still find "slack" roadsters with friendlier frame geometry. Look at touring bikes. If you have one in your area, go to a dedicated "roadie" shop. (Usually, they'll have TDF videos playing on the store's video and a bunch of very high-end frames hanging on the wall....)
My current ride is a very vintage 1970s "Cilo/Swiss" roadster. Columbus steel frame, Shimano 600 components, and a cushy, stable frame geometry.