I don' think this is exactly what you're looking for, but Domainr is my favorite place to try a bunch of different domain ideas. Does a good job of finding options you might like using all the weird domain types.
This just got posted on Product Hunt today and they go above and beyond to answer this question. They really take into account what your business does, potential trademark issues, domain availability, and more. However, depending on what features you want to utilize, you will have to pay for some of them (freemium / saas model).