Hmmm.
The smaller breeds might be a good choice. They won't go 20 miles but that doesn't mean you couldn't go a few miles with them along side and then let them ride with you the rest of the way. There are dog carriers you can tow behind your bike or, for very small dogs and puppies, attach to the frame. Most of the small dogs are packed with energy but aren't long distance runners/walkers. Sight hounds might be a reasonable choice as they're usually quite happy lounging about the house yet are quite comfortable going long distance though you couldn't take any dog 20 miles on blacktop because of what it would do to their pads. If you ride on dirt or grass, then it's definitely doable. Some sighthounds are OK with smaller animals too. While greyhounds are amazingly fast, they're sprinters and tire quickly. As Wikipedia says, ""Forty-five mile per hour couch potatoes." What they can do is lope along beside you quite happily at a moderate pace for longer periods.
In truth, I wouldn't trust any dog to be ok with a small rodent running free. If you take your hamster out of his cage, leave the dogs and cats shut in another room.
Whether the dog runs into the hamster or the hamster runs into the dog, it always turns out badly for the hamster.
Greyhounds may seem larger than your requirements, but again, the large dogs are usually the most docile indoors and don't need gobs of exercise. Wolfhounds can have problems with long distances so I wouldn't consider them and Afghans can be hard to housetrain plus have a reputation for being a bit aloof and very unreliable off leash. I would never take a sighthound offleash in an unenclosed area. You know, a whippet may not be a bad choice, particularly if you have access to an enclosed area for exercise. My brother had one who got along with everybody and loved being near everyone all the time. She was fine with walks but enjoyed running when the opportunities came along. They don't have the housebreaking issues other sighthounds have and they have a sweet disposition. If raised with cats and other small animals, or have lived with them in previous homes, there shouldn't be any problem.
Any dog will be a trade-off but given the need for a docile home dog that doesn't need much exercise but enjoys it when available, is fairly small but not too small or cutesy, doesn't shed much, is friendly to other people, has a reputation for good health, and not a trouble to neighbors, a whippet may just fit you very well. Check out
this article on Wikipedia.
and
National Whippet Association.
When James got his I was like, huh? I didn't think a sighthound would be a
dog dog but she was so affectionate, so fun to be with, that I just lost my heart. Madison was a joy to be with and taught my puppy some very good manners. They may look unconventional but they are loving dogs who will curl-up in your lap but also love to run around. Unlike the terriers and others they're couch potatoes in the house, reserving their energy for going outside. They even use them as therapy dogs because of their pleasant disposition.