Innsbruck is a very good place to stay. You have all the advantages what cities offers you and additionally you have great opportunities to ski. There are a few skiing areas surrounded By Innsbruck.
The nordpark is a very individual skiing area. Most possibilities you have there for freeriding. If you go to the top of the mountain you have very difficult steep runs which are not prepared by machines. You will only find two lifts except from the cable cars and only some official slopes which are red and only one blue slope. The nordpark is very famous to the locals and if there is fresh powder it is the best area to go for freeskiing.
There is also a good park up there. Not so many jumps but quite good and always good visited.
Beside the skiing also a lot of tourist come up to the top for taking photos because of its incredible view you´ve got from above the mountain. To get to the skiing area it only takes about 30min from Innsbruck but then you are also about 1500 meters above the city.