It depends on your interests... Those would be my favorite things to see and do in the old city -
- quartier Petit-Champlain and place Royale
- all the historical buildings, including the churches and the Citadel
- evening walk on promenade Dufferin, near the Château Frontenac
- Musée de la Civilisation (for a rainy day)

Just outside the city, my favorites are
- Montmorency Falls
- Île d'Orléans
- Côte de Beaupré

For events in June, check out http://www.quebecregion.com/en

Enjoy!

www.expedia.co.uk/Quebec-Hotels-Fairmont-Le-Chateau-Frontenac.h12522.Hotel-Information

my fav hotel deals frequently on booking discount sites

Last stayed there on a sale for $150/nt it was awesome!

I think ventdest has some terrific suggestions for you but I would add:

Les Escaliers Casse-Cou (Vieux Quebec)
rue St. Jean just outside the walls (stop in J.A. Moisan)
on a nice day, the ambience on les Plaines d'Abraham

and removed from the usual tourist stomping grounds:
Jardins Bois de Coulonge
Sillery for the peaceful tranquility of the nearby riverfront

Love rue Saint-Jean too, and J.A. Moisan is a must... Stop at the chocolaterie as well.

Also the Image Mill (light and sound show on the history of Quebec) should be coming back in the summer of 2011... http://lacaserne.net/index2.php/other_projects/the_image_mill/

Daniel mentions Quebec's most known staircase (Breakneck). I find that stairs are a lovely trademark of Quebec City - see http://www.quebecregion.com/en/quebec_city_and_area/stairways?a=vis

There is even a yearly challenge for runners... 16 kms, 3,000 steps. Whew!

Manoir de l'esplanade in the old town.Paul

Thank you for all your great ideas. Now does anyone have any more hotel recommendations within the walls?

The Fairmont Chateau Frontenac Hotel (previously mentioned) is a landmark in Old Quebec. It's location is excellent and you can see it from pretty well anywhere within the old walled city, and from a good distance outside which I think is a nice feature for finding your way back through the winding streets. They have a number of different rooms styles, sizes and prices (none of them inexpensive) but beds and furnishings etc are upscale in all. Dining and shopping onsite and all around.

We have also stayed at the Quebec Hilton which is not within but just across the street from the walls and entrance to Vieux Quebec. Many of the rooms have views out over Old Quebec. This is more-or-less a typical Hilton, a modern full service hotel. Our last stay there was in 2005 and it was fine.

A few years ago some friends stayed at the Hotel Clarendon which is also very well located within Old Quebec. I have walked past but not beeen inside myself, however they enjoyed it and recommended it (it was fully booked last time we tried). It is an older boutique style hotel in a Historic Building, so I don't think you can expect new/shiny/modern but they described it as charming, clean and comfortable.

We will be in Quebec City the 2nd week of August and wonder if anyone would recommend staying outside of the old city and staying directly across the river from the Chateau Frontenac in a private home with an apartment? The view looks great and we would have a one bedroom apt that is nice from the pictures. Or will we miss out not being in the old city. I am told the ferry is not far to commute to the old city.