How an algorithm update impacts a local website depends on how the site ranks in the search engines. I previously explained how search engines distinguish between localized and non-localized queries and when thinking of how a major algorithm update like Penguin or Panda may impact a website's rankings these factors can come into play.
If a site is ranking purely organically based on a localized search or a local query like "New York City Pizza" their site's rankings could be greatly impacted if they were to be penalized by an algorithm update.
On the other hand, if a site is ranking as a blended local result via Places search, I have seen websites piggy back off the strength of it's Places listing regardless of an algorithm update. Meaning that while the site may have been severely impacted in strictly organic search results, it seemed to fare better if they query was integrated with Places search.
Maps Rankings vs Organic Search Rankings
Regardless of where you're competing, be it local or national, its important to stay on the good side of Google. Even local websites can feel the wrath of Google and the traffic provided from Google Places is not enough to be enough to supplement the losses from Google's organic search.
If you liked this you might enjoy What Would Google Do?