Spend the day exploring your city. You can take a bike tour, or find a route online to see the sights.
If there aren't any specific routes you both want to try, take a real adventure and make up your own.
Personally, I live in a great area for bikes. One of my favorite weekend activities is riding my bike to the bus which takes me to the train which takes me downtown to the ferry, which takes me to a fantastic island filled with biking paths.
You never know what you can find around you! Discover it together! (& pack snacks!)