Like the others have said, Power BI is capable of meeting your requirements. However, to host it on-premises you will need to purchase 'Premium Capacity' (PC) which isn't cheap. PC will then give you the option of a report server which is on-premises. There is an online calculator to work out the cost of PC.
The key here is web access but securing it on-site. SSRS is one option but it's not an interactive Dashboard. You could use Power Pivot to hook into SQL Server and SSAS. It has dashboard capabilities but they are not as fancy as Power BI. From there you can embed PP in many on-premises hosted services and allow the end-user to hook into that service.