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A 25-minute walk north of town lies Playa Grande, nicer than Taganga's beach but maybe even more crowded (follow the coast line to the north and take the path which seems to end at a house). OsmAnd or Mapy.cz cover the hiking paths. It's better to not flash expensive things on this path during day time. Avoid this hike after sunset. It is also possible to take a boat to Playa Grande for COP$10,000 (can be haggled down, September 2021).
Or take a boat to one of the more remote beaches in Tayrona Park like Concha, Chengue, Neguanje - real unspoiled paradise. There are no people except some fishermen.
This office offers free information in English, Spanish and French. It promotes local operators for short treks, fishing, diving and ecolodges around Tayrona park. The office represents the local indigenous community Wiwas agency which organizes the Lost City trek with an indigenous guide explaining the culture, the Lost City story and the nature of Sierra Nevada. Also a good source of practical Taganga information such as accommodation, restaurants, bars, events and transportation.