Hi Wendy. Without hesitation, I'd choose Hoi An over Hue. Hue is nice, historically important, and has some impressive temples if you have time to get around and see them, but the city itself is far less remarkable than Hoi An, and the Hue Citadel, which is the city's biggest attraction, has not been kept up well. Hoi An, on the other hand, is visually stunning, and it's one of a handful of cities in Vietnam that knows how to manage its tourism. You can buy a single ticket that will get you entrance into multiple historic sites. (Be sure to buy the ticket at one of the sites or one of the official tourism offices. If someone approaches you on the street, claiming to be a tour guide, and offers to buy the ticket for you, you will be overcharged.) Hoi An is also a delightful place to not do anything touristy at all, and simply wander and people-watch instead.
As far as bike tours go, there are plenty of bike rental places around town. I've never taken a bike tour there, but I've had some great rides on my own, just renting a bike and riding outside the touristy center, into the local villages.
Have a great trip!
Dave Fox - Globejotting.com