I posted on another thread about this but the food at Sutro's gets very mixed reviews (yelp.com/biz/sutros-at-the-cliff-house-san-f…), which is somewhat surprising since George Morrone of Fifth Floor took over the kitchen.
I don't think they'd mind Nikes, not sure what your definition of "tourist attire" is. Even on a sunny day (which we've had lately), out at the ocean it's not generally shorts and tank top weather. Other than that, anything would be fine.
I ate at the Bistro a few months back and the food was casual but pretty good (the pop-overs were *really* good). Even that was expensive ($20+ for a crab omelette) but the view was great. However, with the Tut opening, there will probably be a crush of people. Perhaps get a reservation at Sutro's and when you get there see how long the wait is for the Bistro.
We had lunch at Sutro's during Winter Dine About Town. I wore a sportcoat and jeans and my family dressed about the same. There were a bunch of people who were more dressed down than me. Your sneakers shouldn't be a problem (as long as you don't put them on the table ;-)).
The redesigned space is beautiful. We thought the food was very good. It's probably falls short of the very top places in town but it's definitely a cut above the usual tourist spots.
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