According to Wikipedia’s well-documented LGBT rights article, same-sex intercourse is legal in Georgia, Armenia, Azerbaijan, Kazakhstan, Kyrgyzstan and Tajikistan. It is illegal in Iran (death penalty for men, 100 lashes for women), Uzbekistan (3 years imprisonment for men, legal for women), Turkmenistan (2 years prison for men, legal for women) and Afghanistan (probably long prison sentence).
In practice, you would not want to be too open about your sexual orientation anywhere. Although there are pockets of open-mindedness in metropolitan areas where people are young, well-travelled, not religious, well-educated and earning a decent living, the majority of people in Central Asia, the Caucasus, Iran, Pakistan, Mongolia and Western China are not tolerant of anything deviating from recent tradition (homosexuality was prevalent in many areas historically).
Stories of homosexuals being beaten, raped (if a woman) or ultimately murdered are depressingly common.
It must be mentioned that throughout the Muslim world, especially in the strictest countries like Afghanistan, sex between men is often socially accepted (particularly penetrating, not being penetrated), but being gay is absolutely not. In these societies, that is 2 different things.
If you are an LGBT couple traveling, maintain that you are friends to avoid trouble at hotels, and do not ask for a double bed.
Using gay dating apps is probably the best way to find connections. In Kyrgyzstan, be aware that undercover gay-bashers are known to be active on these apps. You might also want to watch out in Iran.
Kazakhstan’s Almaty, Astana and Karaganda, as well as capitals in the Caucasus have some low-key gay-friendly nightlife. HIV-rates amongst gay men are generally high across the region.
In Iran, single male travellers are likely to receive advances from men as well as women. Although you might hear some people say that Iranians are totally cool about homosexuality, the government is most definitely not. Iran’s government has executed thousands of LGBT people since 1979.