You can get to and from Fåborg in many ways by sea and also make daytrips using it as a base. There are regular sailings to the islands of Bjørnø, Lyø, Avernakø and not least Ærø (Søby). You can also go to Als from Claus' village of Bøjden nearby.
The tourist office (with more generous summer opening hours of course) have lots of bike for rent. I suggest a tour of Svanninge Bakker if you can muster up the energy to tackle the hills. Fåborg itself is just as easy to walk around on foot.
As the former railway station has been turned into the bus station, this is the only way to get here by land if you haven't got a car or bike. Luckily, there are several bus lines both to Svendborg and Odense to name the main ones. You can also buy a day card to save money if you are travelling a lot in a day.
if you are coming from or going to ærø then you catch the ferry that connects faaborg with søby on ærø.
it´s a pleasant one hour journey on a little ferry that runs several times a day.