I'm just learning the REST API and am considering using for a friends portfolio site of illustrations. I'm planning to build the frontend using Backbone templates populated at runtime via the API. Bootstrap for the responsive layout.
My concern is that SEO will be less effective than just using a wordpress theme with Yoast SEO plugin. Does anyone have any tips for optimising SEO when using the API in this way?
Everything depends on how you build your frontend.
The most important tip is, that you make sure, that bots can crawl and get access to all of your JS, CSS etc. files. As I understand, basically with REST API you build your DOM and your actual content is not in the source code. So just give access to robots and should be fine.
Please use Google Search Console to test your page with Crawl/Fetch as Google. If there are no blocked recourses and the rendered page looks as expected, then technically Google will see all your content.
Another important tip is just made attention how your final DOM will look like and URL structure, just apply here all necessary SEO strategies.
