Is Spring still a good option for this? Which Java framework has good templating support?
Spring is unnecessary - the Java templating mechanism is called JSP ( Java Server Pages ) and its part of the standard Java package - no additional framework is required.
https://en.wikipedia.org/wiki/JavaServer_Pages
To do this you will need a runtime container like Apache Tomcat. ( http://www.tutorialspoint.com/articles/run-your-first-jsp-pr...)
If you're hell bent on running Spring ( its entirely not necessary ) you can use Spring MVC which is part of Spring Framework.
Here's an example https://www.mkyong.com/spring-mvc/spring-mvc-hello-world-exa...
Spring is fine, and I mostly use Spring Boot for API services. But for web stuff, my personal preference is for Grails (which ultimately is still Spring underneath, but with Groovy flavored goodness on top). At least for server-rendered HTML. If you're building an SPA and using fancy JS frameworks where most of the application lives in Javascript-land, then that might change the picture.