A little more than an hour from Linz is a small village in Styria (Steirmark). During the winter time it is a great place for skiing, but during the rest of the year it is possible to hike up the skiing trails.
It is a wonderful little place for a day hiking trip. There are many trails to chose from for all levels of fitness.
It is also possible to stay for the weekend and there are several hotels in the area. I have personally not stayed in any of these hotels so I cannot make any recommendations.
If you are in the mood for a bite to eat at a cute Austrian restaurant, I would recommend the Passhöhe. Family owned and operated for more than 100 years, this place will not disappoint. However, there are not so many vegetarian or gluten free options as it is very traditional Austrian food.