I must have stayed in at least 100 hostels over the years, all across the USA and in many other countries.
Way back around 1974, I paid the exorbitant price (at the time) of $99 for a lifetime membership.
The US branch of this international ogranization used to be called AYH: American Youth Hostels. Indeed, they used to be specifically for young people. Several decades ago the organization re-branded itself as HI: Hosteling International, as a means of widening appeal to all age groups.
There is no cookie-cutter mold for hostels! While some of the regulations may be the same within any given country, you will very definitely find variations among the amenities offered and the atmosphere of each facility. Also, generally speaking, you will find that locations in city centers will command the highest per-night fees, but still be cheaper than hotels.
You mentioned Airbnb, saying that the cost of places "weren't much better" than $200-a-night hotel rooms. Perhaps you didn't know that there are Airbnbs that offer private guest rooms in other people's homes. I just did a check online via their website and found that there are a few of these in Boston for $65 a night.
At that price, you will have the full amenities of the apartment, ONE host (or a couple) dedicated to YOU, and, most of all, your very own private room with no snoring roommate. For the extra $15, my opinion is that it is worth it.