Some good info here. And yes, there are lots of great options in Austria depending on your ability and wishes. There are almost no uphill trails, so uphill is either riding forest roads, walking up trails or taking the lift. And down there are mostly (boring) forest roads or flowy MTB trails and very challenging hiking trails with very few easy downhill singletracks (not like the North America or Australia where there are lots of easy built trails). If you like challenging downhill you will be very happy.
Bike park and gondolas (uplifts as Finn translated a little unconventionally) in Austria almost always take unicycles (in Germany it’s often a problem). Sometimes unis are free, sometimes you have to pay the bike price and sometimes half a bike
As Finn correctly mentioned, mountain bikes are technically banned from almost all trails. However, this is only for liability reasons, and you will get route info from the official tourist office that goes on many many trails. So you can basically ignore that.
Mountain biking is an important tourist activity in Austria and important for the economy, so there are lots of options and facilities. And unicycles are generally well accepted (although as most places not well known). There is much less of the liability problem that is common in North America.
If you are a technically strong rider, you can take forest roads uphill and then ride down hiking trails. But most are pretty challenging.
About 70-80% of the tracks in bike parks are fast flow trails that are not much fun and pretty sketchy on the uni, as the speed is much slower. However, there are some great bike park tracks, usually the more natural ones that can be challenging and fun.
Komoot is probably a decent resource, but there are many online bike routes, although many will be more endurance bike rides with little technical challenge (look for ones marked as technically difficult).
If you have a few days for muni I think I would recommend trying all three types: 1) a bike park, 2) taking a gondola/chairlift up and riding hiking trails and 3) also try riding 1000m+ forest road uphill and descent on hiking trails, as each has it’s own flavor.
Maybe post what region you want to visit and someone can give more detail info (if you go to Steiermark than you can preride the XC and DH courses for Unicon 2026).