On the nature front, there are really a lot of great public lands on the east coast. They are a bit less iconic than what you can find on the west coast, but you can still hike, camp, climb, ski and beach to your heart's content.
I think comparing SF to DC and Boston makes the most sense just due to similar size. LA and NYC are in a class of their own.
Walkability: for pros, DC is flatter and cleaner. The Metro is cleaner and more reliable than Muni. For cons, the city itself is a bit more spread out, and its hinterlands (e.g. Tysons or Silver Spring), although accessible via public transit, are much less walkable than San Francisco's hinterlands (e.g. Berkeley or Palo Alto). But the biggest issue is that D.C. is just not really walkable in either the depths of winter or the heights of summer (although evenings can be pretty pleasant, and you can actually enjoy an evening out on a patio). Maybe I'm a wimp with low tolerances, but that's six months of the year gone right there.
Diversity: SF is around 1/3 foreign born, while DC is like 1/6 or 1/8. Almost half of SF speaks a language other than English at home, while DC is more like a quarter. DC is diverse, just not as diverse as SF.
I agree with the rest of what you said.
Metro absolutely does not serve many areas. It's a far cry from NYC or European cities, but was totally workable as long as you stuck to the city and certain suburbs.
As somebody who has lived on three continents in major metro area's as well as countryside IMO SFBA has the best dating scene.
I am married now, so I have been out of the single pool for a couple years...but before that I will say that SFBA had the most attractive pool of available woman in the world, if intelligence, creativity, independence, being self starters and physical attractiveness is what you value.
I sure found the love of my life here.
I have one friend who lived at a base in Antarctica for awhile, and he favorably compared the dating scene there to what's in SF.
2) SF & Valley: Diversity. Bay Area cities top the list of largest number of foreign born residents, with only LA and NYC being competitive.
3) SF & Valley: Weather. LA beats us here, but SF trounces NYC, Boston, DC, and Seattle.
4) Just SF: Walkability and street life. SF is more walkable than most cities (the weather helps with that), and although it has shitty public transit options, it's only shitty in comparison to places with actual good public transit, which more or less don't exist in the US.
5) Just SF: Weirdness. Okay, SF has driven out most of the interesting weirdo and artistic crowds and replaced them with CrossFitting Burners. But there are still remnants of that culture, more so than most places except perhaps NYC.
6) SF & Valley: Food. It's mediocre in comparison to the scenes in LA and NYC. But it's still worlds better than the rest of the country.
7) SF: Arts. Similar to food, it's mediocre compared to LA and NYC. But it's still worlds better than the rest of the country.
8) SF & Valley: Nature. West Coast cities are all competitive here, as is Denver/Boulder (though even they lack the beaches), but this is another place where East Coast cities fall short.
In the end, the only plausibly competitive cities on this scoring matrix are LA and NYC. LA sacrifices a lot of the walkability and weirdness of SF. NYC sacrifices the weather, and moving to NYC from SF isn't going to get you of any the much vaunted coupon-cutting decrease in cost of living that everyone in these comments is so pumped about.
Just to be fair, I'll also list disadvantages of SF:
1) Cost of living. "No one is willing to pay that much to live in SF, it's too expensive."
2) Dating scene for men.
3) Travel. Subjective, but East Coast cities are better situated for international travel than the West Coast.
4) Cleanliness. Yep, SF is an unhygienic shithole in many places.
5) Monoculture. Too many tech folks here, not enough diversity in industry.