Look up the technical presenters at your favorite math or stats conference and look at the orgs they work for. That's how you can tell which orgs are serious about solving research problems and spreading solutions.
You could also look into the successful quant trading shops, if you're alright with not sharing results outside the firm. The nice thing about them is success or failure of your work is apparent much more quickly than the timescale of science, and it's harder to spin than other businesses. So the data science that gets done is generally pretty technically legit.