A concern in August would be which hotel has the most reliable AC. There are some bad AC experiences on Tripadvisor at the Sofia Balkan. The Hilton has a nice outdoor pool, neither the Balkan or the Intercontinental have a pool, but the Hilton not as close to the sites and restaurants.

A concern to me in October is that upon 3 consecutive days of weather averaging 55 F, if I remember right,
Bulgaria switches over to heat. In many if not most hotels, individual rooms can not toggle back and forth from heat to AC on an unseasonably warm day. My experience is that hotels in Central and Eastern European countries and Russia are kept very warm so it is very important that the windows open to get some relief.