Typical to all of Latin America, futbol (Soccer to tourists from the States) reigns king. Around the many “Inder” (the recreation division of the Medellin Council) courts you’ll find around Medellin, chances are there will always be a futbol match going on between locals. Feel free to participate as long as you’re respectful.
Medellin also offers almost any major sport you’d play back home. For example, there are quite a few places where you can play pickup basketball almost any day of the week between many parts of the city. When you participate in your first pickup games with locals, I suggest asking someone where, and when, they play more games to snowball your participation. Pickup games will almost always be free.
For the epicenter of sports - head to the stadium off the Estadio station. It’s huge - there is a full-sized track, Olympic swimming pool with hours available to the public, many basketball courts, volleyball courts, soccer fields and much more.
There are multiple golf courses in Medellin but most aren’t open to the public and require a membership (which is expensive, at 660,000 COP a person, not counting the initial fee). However, there are two ways a tourist can play. Asking a private club, such as El Rodeo, to buy a two month membership and, secondly, if you’re staying at a five-star hotel, you can play on the courses the hotel is allied with.
If you fancy hiking in Medellin then you'll want to check out the Medellin Hiking Facebook Group who have regular walks.
Ask around and you're also likely to find some ultimate frisbee groups.