Arriving by plane to Taganga is a metaphore of course! But to Santa Marta international Airport Simon Bolivar, yes, it is possible.
The planes arrive from Bogota, Cali or Medellin but also from Miami and Panama City. The flight duration from Bogota is about 1 hour and the other cities are a bit longer but still short.
Santa Marta airport is small and it can be very busy depending on the time of day, so please advice your airline before you travel. That way, you will have the peace of mind knowing that your journey has been sorted out properly. Simon Bolinvar international airport was completly renew and modernized.
The traffic has increased over time and the prices allow traveling by this mode of transport. The main companies are Avianca which manages now the low cost airline Vivavair and also Latam and other American airlines authorized to operate from there. Then, book on time to get a better price.
When arriving by plane to Taganga, you still need a cab from the Santa Marta airport to Taganga. There are always plenty of taxis that can bring you to Divanga Hostel in Taganga! They usually now know Divanga but you can help telling them that Divanga Hostel is on Google maps and they just follow Google recommendations.