Odense is not only the birth place of Hans Christian Andersen. It is also one of the oldest cities in the country - actually more than 1000 years old. There are plenty of attractions, a lively city centre with good shopping opportunities and many nice restaurants and a lively night life. (from www.visitdenmark.com - an excellent site!)
For most tourists however, visiting the childhood home of Danish fairytale writer Hans Christian Andersen, is the main reason of visiting this city in the middle of Denmark. One of the nice (and free!) activities you can do in Odense, is follow in the footsteps of Hans Christian Andersen through out the city. Also Odense is the no. 1 city for bicycles in Denmark, with over 13000 bikes passing through the center on mornings it is quite a sight!
There is also a zoo in Odense which is in walking distance from the center of town on a nice route along a river, or you can take a boat down the river as well. If you are the more relaxing person, you can enjoy a hot summer day in one of the many parks. Worth to mention is the Fairytale Garden, and Munke Mose in the city center. From Munke Mose, you can enjoy a nice walk trough the old and expensive part of the city along Langelinie, and end up in a place called the Forrest Lake, where you get the best ice creams, with a beautiful scenery.
2 minutes walking distance away, you will find The Funich Village (Den Fynske Landsby), displaying old houses, 1800th agriculture and more.
Odense is the third largest city in Denmark.