In reply to Katzina.W:
Good plan, the more acclimatisation you can get in the greater your chances of success and of a more comfortable summit day.
As others have said a few hours spent at the top of the Midi will have limited effect and there is nowhere you can have a 'brisk walk around' as you are straight onto narrow ridges and crevassed glaciers. ( You could go up and down the steps in the station but really quite limited). I am presuming you will be solo for these first days.
Mt Buet is a great option. You could do it in one longer day but you may find it better to stay the night in the Berard Hut, a couple of hours from the road, and then have a longer slightly slower ascent to 3,000 metres and have a delayed picnic around the summit ( assuming weather holds ) before descending. Expect snow fields but no glaciers, usually lots of Ibex, Chamois, eagles.
A walk up to the Albert Premier Hut, spend the night then return to the valley is a good shout. If you have the skills it is possible to gain some height above and behind the hut without getting onto technical or crevassed terrain before you descend.
If you have done the above and still feeling good and have any spare time you could then get the lift up from the Italian side ( bus service through the tunnel ) and spend the night at the Torino hut, about 3,700 metres. Not much walking around area as you are straight onto crevassed glacier but the coffee is awesome!
Gran Paradiso is good but not a route I would recommend to solo unlike the ones above. As Robert says, you need at least one 4,000 metre peak under your belt before attempting Mt Blanc ( 4,800 metres ). I would assume one or more 4,000 metre peaks are in your itinerary for the week with your group.