I'm looking for an average price per square foot for residential
construction in San Francisco (remodel and/or new construction).

Hello.

"The 2004 edition of the "National Construction Estimator" states that
as of the third quarter of 2003 the cost of construction was $75.71
per square foot. This figure is adjusted by city, Sacramento is +10%,
San Francisco is +24%."
source: ownerbuildercenter.com
http://www.ownerbuildercenter.com/faq.asp

$75.71  + (24% of $75.71) = $93.88 per square foot

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search strategy:
"san francisco" "cost of construction" "per square foot"

I hope this helps.