"Cheap" and "safe for GLBT" don't go together. By the time we've established enough of a presence in a place to make it safe for ourselves, we've driven up the cost of living severalfold. And we tend to do it in cities, which are expensive to begin with.
That said, maybe it's the veteran in me talking, but I feel safer in military towns than in your average small town. In a military town, a huge segment of the population - the one that would typically pose the greatest threat to trans people, the twenty-something working-class men - is overwhelmingly composed of people who are scared absolutely ->-bleeped-<-less of being arrested.
If you're in the military and you get arrested off-base, you get prosecuted twice - once by the civilian authorities, once by the military authorities. If either one convicts you of a serious crime, you lose your job, you lose your security clearance, all of your friends find out, your boss finds out, your parents probably find out, nobody respects you anymore, your career is ruined, you go to civilian prison and then when you get out you go to military prison and then when you get out of there you not only have a criminal record but also a punitive discharge from the military further ensuring you'll never have a decent job for the rest of your life. It's bad news. And it's hard to get away with a crime, too, because nobody wants to cover for you and risk their own career.
Some servicemembers still do commit crimes (DUIs are relatively common, as is domestic violence) but for the most part they're probably the most law-abiding portion of the working-class twenty-something population in the country. And they're drug-free, too. I wouldn't worry about them. You might not like the atmosphere in a military town, but that's a different matter separate from the safety issues.