Nattersee is in the Tyrol, north west Austria not in the South. Karnten is Southern Austrian area, Ossiachersee near to Villach with a caravan is 4 to 5 hours away with Caravan varying which of the 3 Routes you use. The longest mileage is 219 which is shortest time and I think better with a caravan taking 4 hours 18 minutes according to Via Michelin.
Nattersee near to Innsbruck indeed has in a wonderful area and with a car there is lots and lots to see you can easily stay there a week and not see it all.
If anyone would like list and details of this area I can send it to you if you email me dvphillips14 at hotmail.com too much to write on here.
Austria is our favourite Country to visit and have been going there for over 35 years the later 13 with a Caravan.
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We stayed at Nattersee for 2 nights in a mobile home while touring Europe on a motorbike & booked it through Eurocamp,it was a beautiful & clean site with excellent toilet/shower facilities,swimming in the lake etc,i would suggest having a look on Eurocamp Independant if it interests you.
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.