I think Seattle, despite not being as close to the mountains as SLC, wins out over SLC by far when considering the elevation difference and dramatic-ness of the landscape. Anchorage is the overall winner.
Seattle:
City elevation: 0
Highest nearby peak: 14,411' (Mt. Rainier)
Prominence: 13,246' (highest in contiguous US)
Distance from CBD: 57 miles
Then, in addition to Rainier, Seattle is closer to the Olympics (7000' of prominence), and the Cascades (10k ft of prominence) than to Rainier. Rainier, amazingly, still dominates them because of how tall it is.
Rainier:
Cascades:
Olympics:
And I say this as someone who grew up in the rockies (in Montana), and has spent a lot of time in Denver and SLC. The rockies are impressive, but there is something other-worldly about being at sea level and seeing 10,000 ft. mountains only 30 miles away, and 7,000 ft. mountains in the other direction, also only 30 miles away. And Rainier is an absolute mindfuck.