Last time I was there was about 8 years ago, and I recall that the glaciers were retreating then at quite a rate, so things may have changed.
However I do recall the following excursions I’ve done over the years.
These were all taken from leaflets picked up at the tourist office when we arrived.
If you are going to Chamonix you must spend at least a week there and soak up the unique experience.
First of all “go wander”, walking around the outskirts of the town we found farms where they would set up their own little bistro, you may see a wooden sign that just says “Raclette” and the farmers wife will cook it for you, at a reasonable cost, yum. The one thing I love about France is that they enjoy sitting around eating good food and doing bugger all.
Excursions
1) On foot head NW out of the town, over the river Arle and up the valley side, then head south following the valley. You can carry on, then descend to Les Houches, and return via road to Chamonix. All well signposted, you don’t need a guide, just good footware, and 2 litres of water as it’s a good day walk, no ice or snow.
2) Drive north out of Chamonix to Barberine (or anywhere further than Argentiere) or thereabouts, find somewhere to park and then just go walking in and out of France / Switzerland. Lovely alpine meadows, you can almost see the Trapp family and Julie Andrews, no ice or snow.
3) Take the rack railway to Montenvers (a thrill in itself) to Mer De Glace. Get a return ticket and take time to walk to the lip of the glacier (about 30 mins) and admire the view. No special equipment required.You can pay extra to visit the “Ice Cave” which is sculptured out of the head of the glacier and a bit touristy but worthwhile.
If you have; crampons, ice axe, rope, and know how to use them, go down the ladders on the valley side and onto the Mer De Glace and just take a walk, awesome solitude and big nature in the raw.
4) On the south side of the valley we walked to the Bossons glacier but a bit dissapointing; you could gaze at it but it was receeding, and may not be viewable now.
5) Aiguile Du Midi, the first time I was there I had to phone a friend to get a loan to afford the ride on the cable car to the top. There’s not much there (just the cable car station) but being at altitude (13,000 ft) is awesome, as is the view of all the surrounding mountains.
If you have; crampons, ice axe, rope, and know how to use them, go down to Valee Blanche and enjoy the solitude, if you have a day try to make it to the Refuge Des Cosmiques, more awesome views, and a chance to get a unique sticker for your camper (if you collect them).
6) If you have a “really good” sleeping bag and a bivi bag, take the cable car to Grands Montets and spend the night on the ice. I did with my son before we went on a climb the next day. The night sky was awesome, you can see the Milky Way, and watch satellites passing overhead.
Never mind all this, go spend a week (at least) in Chamonix and enjoy it.