In reply to andynees:
- Go on one real hike / climb which is reachable from the city and do-able in 10 hours or less
I'd recommend one of the many exciting opportunities in the Aiguilles Rouges, any of the peaks there from the valley are a good 1300-1500m ascent, and some of them have some decent climbing/scrambling/soloing. The slightly harder ones to get to, though still easy enough to do on your own with not much knowledge of the area, are the Aiguille du Belvedere or the Grande Floria, or the traverse of the Aiguilles Crochues.
But if you want to sleep in a refuge, you might want to aim towards the winter room of the Albert Premier (the actual refuge is now closed) on the banks of the Le Tour Glacier, but take a slightly longer route to get there... try going up to the Aiguilette des Posettes from Le Tour or Montroc, going over the Tete du Balme and down to the Col du Balme, then along the high traverse path to the refuge (you should see what routes I mean if you have the IGN map, or just trawl through camptocamp). You'll most likely meet a few people there who are doing the Chardonnet or Aiguille du Tour, who would probably share some knowledge, advice, and opinions with you for future trips, in return for a couple of slugs from a tiny bottle of whisky.
There is currently enough snow and weather about in the 2000-3000m altitude range to make either of these plans feel exciting and like something of an accomplishment, without them being too dangerous.
I'm currently in Ireland and not back until after the weekend, otherwise I'd gladly throw a map and some hints your way.
Best of luck!
edit
Ah, just noticed your timings, in that case I'd head straight up to the Albert Prem on the horrible moraine path (two to four hours, depending on luggage and fitness), enjoy the pretty sunset, and set off on the hike that I suggested, but in reverse, the following morning.
Post edited at 10:25