Allocations on many supercomputers through XSEDE, or also directly at some, including Cheyenne at NCAR and Frontera at TACC. These are all free of charge to you, and also provide support and training.
Virtual machines, storage, and other cloud resources, including Amazon Web Services (AWS), Digical Ocean, and Google Cloud. These all require a credit card for the charges, but can be cheaper and more convenient than your own hardware. AWS is very comprehensive and has a fast interconnect suitable for a cluster, while Digital Ocean is cheaper and much more user friendly. Google developer account provides access to useful services such as the Google Maps API.
Google Colab is a free Jupyter notebok service optimized for machine learning.