At MDE, stay airside—José María Córdova is far from the city, so relax and stay near your gate.
A 3-6 hour layover in Medellin is not recommended. Jose Maria Cordova Airport is 28km from the city in the mountains - the road takes 45-70 minutes even in good traffic. By the time you clear immigration and travel both ways, you will have almost no time in the city. Stay at the airport unless transit is confirmed smooth.
Six to ten hours makes Medellin viable with careful planning. Taxi from the airport ($17-22) to El Poblado neighborhood. Walk the Parque El Poblado area and the Provenza street for cafe culture. The Botanical Garden (Jardin Botanico) in the north of the city is free, peaceful, and beautiful. Take the Metro to Acevedo station and connect to the Metro Cable for views over the comunas - an extraordinary urban landscape. For food: bandeja paisa (the full traditional platter), arepas, and Colombian coffee everywhere. Allow 2 hours for the return trip to the airport.
With 10+ hours, go beyond El Poblado. The Pablo Escobar narrative looms over the city but Medellin has moved dramatically beyond it - the cable cars and outdoor escalators serving the hillside comunas (built as social infrastructure) are a genuinely inspiring story. Visit La Sierra or La Aurora cable car for the community experience. The Museum of Memory (free) covers Colombia's armed conflict with dignity. Laureles neighborhood is more residential and less touristy than El Poblado - better food prices, more local atmosphere. The city's flower festival (Feria de las Flores) in August is world-famous but the city is worth visiting in any season.