ETA: It looks like you want to skateboard along the embarcadero, which might give you some leeway. I remember the city touting that as a "Boardwalk" type of place for people to walk, jog, and (roller)skate back in the day so it might be okay unless anyone remembers seeing specific "no skateboards" signs?
I might be wrong, but I believe the citation below is still the law in SD and most of downtown would be considered "business district":
Section 84.12 (a) of the City of San Diego Municipal Code states: “It is unlawful for any person riding on roller skates or by means of coaster, skateboard, toy vehicle, or similar device, to go upon an open roadway in the City of San Diego, or upon the sidewalk or public plaza in any business district, or upon any inclined surface area of any City-owned or privately owned parkade..."
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Here's an article from the San Diego City College paper that indicates the code section was still valid at least as of 2012: You are not allowed to view links.
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LoginAs with all things, YMMV on whether the cops would hassle you but even if it were allowed, I agree with most of the posters that it would not be very safe (for you or others) with all the people around.