Social life is largely what you make of it in college, given the time you are allowed after you take care of your first priority, your studies.
UChicago and Caltech are particularly academically rigorous, and Johns Hopkins can be. If learning is your top priority, I think those three are your best bet. There is plenty of fun to be had, and culture to be experienced, in Los Angeles, Chicago and Baltimore. And yes, they all field varsity sports teams, just not at the highest level of competition (though still probably fun to watch).
Washington and Texas can be rigorous if you want them to be, but these are more the traditional large public universities with solid academics, huge sports and party scenes. The learning environment is not as intimate as it is at the three aforementioned private powerhouses: classes will tend to be larger at Washington and Texas, individual meetings with a professor will be more difficult to obtain, etc. Austin and Seattle also offer plenty of fun and culture.
Weather:
UChicago and JHU are temperate: four seasons, featuring a mix of sunshine and precipitation, warm and cold weather.
Caltech features the California climate: warm but not often too hot, sunny the vast majority of the time, dry, not much rain. It is nice, but I would find it monotonous.
UW-Seattle’s weather is probably similar to London’s: lots of rain, some snow, but it rarely is too hot or too cold. (at least, not nearly as cold as some of the weather you’d see in the Midwest or Northeast US).
UT-Austin’s weather is a fair mix of sun and precipitation. Summers are characterized by very hot, humid weather – some find that uncomfortable. During the school year, temps are mostly pleasant – not too hot, not too cold.
I think if you are primarily interested in a rigorous, nurturing academic environment, in a four-seasons climate, your best bets are UChicago and JHU.
If you want that academic rigor but in a California climate, it’s Caltech all the way.
If you want the traditional large public university featuring an active party scene and big-time sports, with slightly less of a focus on academics, choose: Washington, if you prefer cooler temps and more rain; or Texas, if you prefer hotter temps and less rain.