Repetitive actions that don't require any degree of concentration can enable you to "zone out" and open your mind to relaxation. Taking that a step further would be focusing your thoughts - rather than allowing the chatter to consume you.
I find that riding my bike allows me to tap into that ability to relax the activity of the mind. I often watch TV or read while I'm on the treadmill, but while I'm outside on my bike I can take in nature, the quiet, and relish in it all. The longer I ride, the more "meditative" it seems to become.
If it has been years since you've ridden a bike I say give it a try. I only ride in neighborhoods. I wouldn't dream of riding on any major road...I think that is better left to the well seasoned, hard core bikers. I would also like to caution people against listening to music while riding or running/walking. I think it is important to hear what is around you at all times.
I recently received my "Surf OM Cruiser" for my birthday. In keeping with the description of my new bike I named her Gidget (After the famous role played by Sandra Dee in the 1959 movie and later followed up with the TV adaptation played by Sally Field- which was filmed in Malibu).
Here is The Surf OM Cruiser.
Here is a picture after I outfitted her with some flowers and a basket.