I suppose I'd think a bit about what you think of as typically "Canadian". What kinds of things do you want to see?
The prairies are kind of impressive, and there are some nice things in the cities there, but they are probably not going to compare to a city experience in the UK. Alberta has the mountains which are quite amazing, and cowboys, but while Calgary is ok it's probably not any more interesting than you'd see at home.
Lots of people as you can see love Vancouver, It's very large, expensive, on the water, a very modern city. There is a lot of homelessness similar to places like Seattle though you can avoid it.
The North is pretty amazing if you like outdoors stuff, but there will be a lot of blackflies in the summer. The long days are really neat though.
Ottawa is nice, the Great Lakes are nice, the Niagra Valley is nice if you like wine.
PEI is very charming and rural, lots of stuff for tourists.
Quebec is totally different, Montreal is an exiting, and in many ways rather European, city. Quebec City is also very charming, more French than Montreal.
New Brunswick is fairly rural, more well known for winter activities but pretty.
Nova Scotia is older, so the main city is more of a mix than some of the western cities., and there are a lot of historic sights. There is a growing wine industry and a lot of small craft breweries. A number of good music festivals.
Newfoundland is very different in some ways, St John's is a very charming city and the landscape is very beautiful in a stark kind of way.
The Atlantic provinces overall have a better music scene, IMO.