At Carol Health, we use a provider called Healthcare Blocks to manage a HIPAA compliant environment in AWS. They take care of most of the infrastructure compliance. While, we take care of the application side. Datica and Aptible are direct alternatives to Healthcare Blocks.
Those options would give you a more traditional hosting route. You could also use a services like True Vault. It's kind of like Stripe for HIPAA data. All of the HIPAA-sensitive data is communicated directly to TrueVault. Your server then deals with non-PHI data.