Sønderborg is located not very far from the Danish-German border.Just south of the border is the German town of Flensburg, which is popular amongst Danesgoing to Germany on a one-day trip, often to shop and to buy alcohol and chocolate, which is cheaper in Germany than in Denmark.
By public transport
From the central bus station rutebilstation there are buses run to Dybbøl, Kær, Stenbjergparken, Kløvermarken, Skovparken, Sønderborg Sygehus Hospital twice at every hour. One way ticket is 17 DKK and payable onbard, only cash. There is also 10 clip card for 120 DKK, if you plan to travel more frequent. One other thing to note is it that, since it is a small town, buses take off twice an hour mostly.
Bike
Sønderborg is a very bike friendly city. Almost all roads have separated bike lanes. Hop up on your bike or buy a second hand one and do not suffer in the buses.