We are hosting 32 websites in one Standard web hosting plan mode and a Small instance size. Will it cost us more to enable "Always On" in one or all of the websites?
Azure unloads your site if it is idle for the standard 20 minute timeout, which can cause slow responses for the initial site users after it is unloaded. Enabling Always On essentially causes Azure to automatically ping your site periodically to ensure that it remains in a running state. There is no charge for enabling Always On, but is not an available option on lower end plans. I suppose in theory it could consume more CPU cycles and thus could require the deployment of more infrastructure if you have many, many sites.
As an aside, "Always On" for Azure websites should not be confused with AlwaysOn Failover Clustering/Availability Groups for SQL Server.