In reply to mart:
Some ideas, but you might already know these.
Chamonix
La Jonction (daytrip)
Ag Crochues and/or Ag du Belvedere (daytrip airy scrambling required)
Aig du Genepi (from Albert Prem hut, daytrip or overnight from valley)
Domes du miage (1st Peak only which is closest to hut/bivvy: no glacier but steep snow/ice near top)
Petit Mt Blanc (Bus through tunnel Italy bivvy en route)
Couvercle Hut (if happy with exposure of ladders -- or do it with VF kit)
Aig Gouter ** see below
Saas
Lagginhorn (W ridge walk/scramble, bivvy at bottom or daytrip - have done as both)
Jegihorn (Normal and/or VF South route)
Mischabelhorn (to hut or just above)
Zermatt
Mettlehorn (daytrip)
Oberrothorn (daytrip)
** If you ignore cable cars and trains the walk in from Chamonix/Les Houches to Ag Gouter summit is a great 2 day expedition (camp at Tete Rousse free site - depends on time of year whether full or not) to almost 4000m. BUT you would need some good scrambling skills and a bit of alpine nous so as to go up/down the grand couloir at the right time of day/night and know how to do it safely with other people about. And pref a helmet. So you need to do a bit more first. But is quite exciting with all the buzz going on. Breakfast snack at Gouter hut then back down while all the rest slog it out for the top or fail. Or just go up and back to TR hut if you don't like scrambling or are not up to the alpiney bit. That's still a good hike from Les Houches.