During the day
When exploring the city, Plaza Botero is nice starting point. On that square are the enormous oversized statues made by Botero. The museum de Antioquia is also quite interesting.
Take the Metrocable for spectacular views over the city. It will go over the poor areas up the hills and shows the differences in this city between the rich and the poor. It's not really necessary to exit at the endpoint, you can take the cable car straight down the hills again.
Laguna de Guatape is a beautiful nature area outside the city.
And then there is the Escobar tour. We knew a bit the stories, but when doing the tour and seeing the actual places was quite impressive. We would recommend a private tour. The subject of Escobar is very sensitive. Not all local people appreciate these kind of tours.
Gay nightlife in Medellin
The Colombians are very friendly people. And we love the latin spirit. But still be very careful, especially at night.
The area in Park Lleras if a good location to start the night. Here you find many restaurants with terraces in a very green environment.
There are some gay bars / clubs nearby.