I don't think that's true at all. San Francisco has an especially major cultural, historical, and tourism presence. Moreover, given we're talking nationwide, I think it's not just appropriate but prudent to consider the San Francisco Bay Area (its CSA that I think has a coherent, pretty singular identity on a nationwide scale), which has both the 5th-highest population in the country of any CSA and has an enormous nationwide and global presence in technology and education.
Atlanta isn't even on the same level (and I don't mean based on the GaWC I'm about to discuss). Funnily, going by the GaWC classification, I was possibly overstating DFW (I consider globalization a big component given we're talking nationwide in such a globalized nation), but I think that's the only mistake I make there. I think New York, Los Angeles, Chicago, and San Francisco are solidly the first four.