What is the best way to get to Avezzano from Rome? And are there places to stay in the city of Avezzano? I would rather not rent a car.
Here is a guide to transport
https://www.rome2rio.com/map/Rome/Avezzano
If you click on the "hotels' tab it brings up an expedia page with 82 listings
There are multiple direct regional trains from Roma Termini that get you to Avezzano in about 2 hours. They depart early and in the afternoon. Check the Trenitalia website for details. The town has a population of 42,500 people, so there will surely be hotels and other similar lodgings. Try Google Maps to get an idea of your options. A guidebook such as Lonely Planet or Rough Guide might have recommended lodgings.