Seems like not to many fellow GLTB FT'ers have been there...
While I haven't been there for a while, everything that I've heard is that the situation has improved a 100%. My advice: you have to be cautious and know where to go since you are not going with a local or someone who knows the city. (are you?) If you stay within recommended areas, you should be totally fine and will have a blast. People there are very friendly.
I'm not too familiar with Medellin, I just know that El Poblado is a good neighborhood, probably where you want to stay. As far as Bogota goes, stay in the northern part of the city (El Norte) which is where all the nice and safe areas are. Think about Polanco if you've ever been to MEX. The city is quite big (10 million people) so there's a good mix of everything and options for everyone. Like I said, the most important thing is to know what neighborhoods you are going to. Do not go to "El Sur" which is known to be more dangerous (if you don't know your way around). When I lived in BOG never went to that area - I would get lost there.
As far as El Norte, there's a bunch of good restaurants, bars and stores for you to see, go out and do some shopping. The nicest malls are Unicentro, Hacienda Sta Barbara and Andino. This last one was the most popular one and where all the 'preppy' locals hang out at. Good restaurants and bars are located in Parque de la 93 and Zona Rosa. These areas and Andino are all pretty close to each other and shouldn't be more than 30 min cab ride. They are safe and you can find lots of dirty cheap 5 star restaurants. Be aware of BOG's traffic it gets really bad - there's a driving restriction during rush hours (if your plate ends with an odd number you cannot drive on Mon/Thur and if it's even, then Tues/Fri, or something like that). Try not take any cab but from the hotels and restaurants (ask them to call you one) since you are not familiar with the city.
There's an area call Chapinero where most of the gay bars/clubs/saunas are. I haven't gone out to gay places there so I cannot recommend one over the other. Chapinero is between El Norte and El Centro (downtown), it should be safe but gotta be more cautious than if you were in El Norte. You can also go downtown during the day to see the touristy places like La Candelaria, a neighborhood from the Colonial times, very nice architecture.
As a solo traveler, if you speak Spanish you should do fine. Do not talk strangers and be careful what kind of people you meet up with. People are very friendly but some of them are jobless and may go after your dollars, just know who to talk to - like in any other city in the world.
PM if you have specific questions. Enjoy and report back when you are back.