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Nice
Places to Stay
 
HI Nice Camelias - http://www.hihostels.com/dba/hostel020173.en.htm

I stayed at the HI in Nice. Very nice place, clean, friendly, good breakfast, BUT it's on the top of a steep hill way up in the city and the bus stops running before 10pm. So, unless you want to spring for a cab, you're stuck.

On the upside, that means that the hostel is very active in the evening with a lot of people staying in, cooking and chatting.

I'm a pretty strong walker, but the walk down to the town was about an hour so I can't even imagine what it's like going up.

So I give the HI a qualified recommendation - great if going out at night isn't really your thing.
 
Day Trips
 
Why not go to Spain since you're it's close from Nice? Barcelona is a lot of fun, Madrid has a wild nightlife, and you may be able to fit in Ibiza too.
 
I found out it's about a 20 hour train form, Nice to Austria
 
The easiest way to get to Nice is to go via Paris. There are night trains that way you aren't missing your days worth of activities and also you won't have to pay for a night at a hostel.
 
Nice to Salzburg, there's some very interesting places. For example, Switzerland!