I think there will be a new airbnb. Before airbnb there was vrbo.com (which is still up - just not as popular as airbnb.) I've used both because my mom is a frugal genius and hates hotels. Especially in cities like NYC, you can get a furnished apartment for a great of the price compared to the shoebox hotel. She still rents from AirBNB when my brother is playing in cities outside Durham and the other team moms are always jealous that she has a full kitchen and ability to sleep. There are rarely party animals in the AirBNB places, unlike the crowd you find in a mid-range hotel in a college town.
I'll have to try this out sometime. I've done it in other countries, but I didn't know that this was a thing in the U.S. until I saw this post. I'm aware of couch surfing, which is ok for the short-term, but it's nice to know that there are other levels and other options.