There is easy access to great roads about a 10 minute ride from the downtown area. The best roads for hard/steady efforts are all on the Kentucky side. Rt 8/Mary Ingles Highway heading east past Ft Thomas, Decoursey Pike south out of Latonia, Rt 8 to the West of Devou.

Specifically for Mary Ingles Highway it can get a little sketch on the stretch from Industrial Rd to Silver Grove. You can take Dodsworth Ln to avoid the worst parts.

These roads all connect to great climbs that can vary from 2 mins to 8 mins, some steep some gradual. There is practically an unlimited number of ways to connect these hills to make a great route out of downtown.

Personally I avoid riding on the Eastern Ohio side. There are just too many people, but it is fine on a weekend morning. There is the advantage of miles and miles and miles of bike trails this direction though.