Lodging, sightseeing in Chamonix/Annecy

Definitely take the Aguille du Midi up to Mont Blanc and take in the spectacular views! If you're adventuresome, do some glacier trekking with a guide. Experience of a lifetime!
On the same side of the valley you can take the old cogwheel train up to the Mer du Glace. It's a glacier that has been a tourist attraction since the 1800s. Sadly, it has receded extremely dramatically. There was a 20 year gap between the first time I saw it and when I went back this summer - if you want evidence of climate change, the European glaciers will give it to you. See it while you can...
Another beautiful place to visit is Lac Blanc, on the other side of the valley from Mont Blanc and the Mer du Glace. June might be a little early to hike to it because of snow but, with the light winter they've had in the alps, you may be able to get to it. It's one of my favorite places in Europe. You can have lunch on the deck at the beautiful old refugio - the views are some of the best anywhere. Glaciers, alps, snowfields...pretty unbeatable.
If you like paragliding, there are many companies that will take you flying over the valley.
The main street in Chamonix is a pedestrian street with many shops and restaurants. It's a nice place to have a meal and people-watch.

Anita,
That was my exact initial plan of things to do in Chamonix, until I learned that in late May the hiking trails are not open. Winter/Spring in the Alps is late compared to the Sierra's. Will have to plan another trip in summer to experience Mont Blanc!
Chris

Ditto Anita on going up to the Aiguille du Midi. 12,600' and one of the best views on the planet on a clear day. For lodging, I recommend the L'Oustalet. Owned and managed by two sisters (siblings). We've stayed there and it was just great. Free parking if you have a rental car. Two blocks from the lift to Aiguille du Midi. It's not in the center of town but a 4 block walk that goes under the rail tracks will put you there. A lot of the city is blocks and blocks of really nice shopping areas. You can spend a lot of time just walking up and down the streets. For food, I suggest Le Caleche for casual dining and Atmosphere for nicer dining. We had nice dinners in both restaurants.

We liked Hotel L'Aarve in Chamonix--I think it is/was in RS guide. Our room overlooked the river, had a small terrace, and was an easy walk to all sites. The IT there is a good first stop for map, etc. Mid June will be a good time for a visit. We were there in late May and found some things closed--including a few restaurants.

Thank you all. I have booked the Hotel L'Aarve in Chamonix and will report back. Looks nice.