Take the metro into the center of town to visit the Museo de Antioquia and Plazoleta de las Esculturas. Afterwards head to the Jardín Botánico for a picnic or eat at its restaurant In Situ. Next walk up the road to the Casa Museo Pedro Nel Gómez. In the evening head to El Poblado for some drinks and a fine meal.
Dedicate your second day to Medellín's remarkable urban transformation beginning with a visit to the Museo Casa de la Memoria to give it all some context. Grab a bite in the center at the legendary Salón Versalles before taking the metro to San Javier for a tour of the formerly off-limits neighborhood of Comuna 13 and to see the area from above in the cable car.
On your third day head out of the metropolitan area to spacious Parque Arví or take paragliding flight over the city from San Felix before checking out the Laureles neighborhood and its many restaurants in the evening.