Gay hotels in Rome are booked by most travelers around the Colosseum, because from here it is not far to the Gay Street on Via San Giovanni in Laterano and at the same time short to the major sights. In the Celio district, scene and sightseeing are close together, which is practical for a first visit to Rome. There are only a few pure gay hotels in Rome. Instead, queer-friendly and gay-friendly houses are spread all over the city center, and a double room for two men is not an issue anywhere.
If you like it a little quieter and more bohemian, Trastevere is the place to be, where there are pretty apartments as well as the second cluster of queer bars. Many travel guides advise against Termini Station and the Esquilino district. The area is not very inviting at night, even if the transport connections are good. For classic sightseeing, the historic center around the Pantheon and Piazza Navona is ideal, where you live centrally but more expensively. Which location suits you depends on what is in the foreground: scene and antiquity are best combined at the Colosseum, relaxed flair can be found in Trastevere. Plan early if your visit falls during Roma Pride, as central houses are quickly booked up.