Cup and cone is actually a good design that usually lasts a long time. Its possible that you have damaged cups or cones in your hub, or just need new balls, but its also possible that it feels rough because the LBS did a bad job adjusting them (if there is significant play in the axle, thats just poor adjustment). So if you only want new wheels because of your hub issue, those hubs might be salvageable and its a job that is pretty easy to do yourself.

For budget wheels made from good components checkout Velomine.com, although I would point you at wheels built on shimano 105 hubs, very excellent but cup and cone design you say you don’t want. .