I'd like to move my WebRole on azure to use one of the new D-Series VM's to take advantage of the faster CPU's and SSD's.
Is there any IIS configurations that would optimize running on an SSD or can I assume that just moving to an SSD will increase performance?
I'm running a single website inside IIS on IIS 8.5.
Just moving to SSD will increase performance on disk io intensive tasks. To be taking advantage of the SSD's, you application has to be performing disk intensive tasks on the web role. Typically web roles use very little actual disk unless there is a database hosted on the same server. As I am assuming you are using Azure Cloud Services, I doubt this is the case. Therefor, I think the SSD's will likely not increase your performance significantly due to the use case.
That said the bigger better faster CPUs most definitely will help out a web role. The sheer CPU speed will help, as will the ability to use all CPU's. To really drive performance make sure you kick off longer tasks on background threads, which will get allocated accordingly.
Hopefully that helps.