In reply to Removed UserLordBaller:
If you are staying at a campsite you get free local bus / train travel which is really useful. Many campsites available, I would suggest the one in Argentiere might fit the bill nicely. Lots of walking accessible from the campsite.
So many day walks and ways of linking, you almost need to identify what you want to see and then choose your routes around those. This site may help: Hiking trails - Chamonix Mont Blanc tourist office, France
Two of the classic, spectacular walks would be the Balcon Nord and the Balcon Sud. These are high level traverses each side of the Chamonix valley. You can walk up, along and down one in a day ( or take uphill and / or downhill transport if you prefer ). A lovely walk could go from the campsite up towards Lac Blanc, along to the Brevent and walk down to Chamonix for free bus back to campsite. Alternatively take the bus to Cham first then walk ( or lift ) up to Brevent and walk along to Lac Blanc and stay the night in beautiful hut right by the lake. Bonus being the walks are much quieter as soon as the lifts stop operating and plenty of wildlife to see; Ibex, Marmots, Eagles. Next day you could descend to campsite.
You can get really close and personal to glaciers and the big cliffs on the Balcon Nord. Walk ( or train ) up to Montenvers. Visit the Mer de Glace if you wish and are happy with steep ladders. Then walk along to the mid station of the Aiguille de Midi. You can walk down to Chamonix, take the lift down or even stay the night in the excellent Plan Aiguille refuge.
You could link these routes together from your campsite by walking or bus to Chamonix, get up to Balcon Nord and stay at the Plan Aiguille hut. Descend to Chamonix and go back up the opposite side of the valley to Brevent ( lift or walk ) and walk along to Lac Blanc to stay the night. Descend back to campsite.
There are so many walks accessible from the campsite such as the Berard Valley including visiting the summit of Le Buet at just over 3,000 metres ( no glacier but sometimes snow patches ), walking up to the Argentiere glacier snout and onto the glacier ( no ropes needed ), walking up to the Albert Premier Refuge with spectacular views of the glacier.
I do suggest checking in on line or by visiting the Office d'Haute Montagne ( OHM ) to check up to date trail conditions and ensuring huts are open. Sometimes there can be snow on the trails which ( if in the shade or early morning ) can be quite icy before the sun softens them.
High Mountain Office - Chamonix-Mont-Blanc Health, emergencies Chamonix-Mont-Blanc