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Iceland is in the Schengen zone and follows the Schengen visa rules, which gives visa-free access to US nationals for short visits.
If your destination in Europe is another Schengen country, you will have to go through Schengen immigration in Keflavik anyway; the onward flight is treated as "domestic" as far as immigration checks are concerned.
If your connecting flight is to a non-Schengen country such as the UK, you have the option of staying in the airport terminal and not go through immigration.
Note that Reykjavik is quite some distance from the airport -- the bus ride is 45 minutes and buses may not depart frequently, so keep transportation time in mind when you decide whether an excursion to the capital will be worthwhile.