Aarhus is surrounded by beautiful beech forests; take a walk in Marselisborgskoven or in the deer park.
As a coastal city, there are many beaches to walk - just remember warm clothes October through early April. There are history trails from Moesgaard Museum right down to the water, with reconstructed stone age, iron age and viking houses and tombs, rune stones etc.
The local soccer team AGF, plays their home games at Atletion (http://www.atletion.com/), which can hold around 21.000 in attendance. If you're a soccer fan, don't miss a home game Played on Saturdays or Sundays as the atmosphere is amazing during game night!
Djurs Sommerland
(http://djurssommerland.dk/), amusement park has Denmark's largest rollercoaster. Can be reached with buses 121, 122 and 123 in 1h15m. Discount if buying your entrance ticket in the bus you only pay DKK 20,- extra for the bustrip there and back.Ebeltoft
is a quaint little town about an hour bus ride away. You can catch bus 123 with a day ticket costing DKK 125 note that you can use this to also get out to the airport if arriving/leaving the same day. It has one main cobblestone street lined with shops and cafes and you can visit the glass museum it has a mirror room that you can walk in! or the world's longest wooden ship. The actual bus ride there takes you through some lovely green hilly countryside too. Just make sure you get off at the station called Ebeltoft C rather than waiting till the end of the line which is the Ebeltoft bus station... unless you enjoy a bit of a walk which one could say is a nice way to view the residential streets one wouldn't normally have done!