I have a SQL Server with many databases on it, the databases run a wide variety of sizes and activity.
It would be great if there was an application or SQL script that I could run to advise me on recommendations of size and costs to migrate to Azure.
At the very least if there are scripts I could run to get a sense of how many "DTUs" I would need. (I don't quite get the concept)
This is a pretty good site that provides a calculator for DTU's based on performance analysis.
You will need to decide first whether you are looking at single SQL databases or an elastic pool. By the sounds of what you are looking to move an elastic pool might be your best option if you have varying sizes and performance requirements, and your total DTU count will fit within a pool (or spread over multiple pools).
The DTU calculator was created by Justin Henriksen at Microsoft and you can get more detail on it here.