score:3
Val di Sole in Northern Italy (near the Dolomites) is a great place for hiking and has some excellent bike trails, as well. Also, the valley's Noce river is perfect for whitewater rafting, if you're trying to mix up your sports activities.
Upvote:1
I like the Virgental in Austria for hiking. It is reachable through the trainstation in Matrei, at the entrance of the valley, if I have Googled correctly.
The north side of the valley is the west part of the Hohe Tauern, the highest mountain range in Austria, including the Grossvenediger (3674m, 4th highest in Austria). The south side is somewhat lower, but for instance LasΓΆrling is 3098m and quite hikeable, and this side has a great view of the mountains on the north side.
There are lots of mountain huts connected by hiking trails, and according to the linked site there are good mountain bike trails as well, though I've never done that.
There are hotels in the valley, but you can get a "Huttentaxi" to get up to a first hut, these are 4WD cars that can probably take a bike too, but you'd need to check that beforehand.
Most huts have private rooms, but if those are full you might have to sleep in the dorm rooms. Call ahead (also if you're going to hike from one hut to the other, call ahead in the morning so your destination hut knows you're coming and can ring alarms if you don't show up).
Unfortunately, it's not cheap. You can easily spend 100 euro/day on rooms and food.
Edit: Only now do I notice the date on the question...
Upvote:3
I like to think Croatia is a part of Central Europe as well so I could recommend a bunch of places to go hiking and biking. If you would consider it, I'll update my answer with a couple of places.
Depending on how experienced you are with biking, you could even start your trip in our capital, Zagreb and then head towards our seaside. On your way there you get to ride your bike through Gorski Kotar which has amazing mountain views and a couple of great and refreshing lakes and rivers.
You could also head east and visit Slavonija which is predominantly flat but has some nice hiking/biking spots here and there.