If you want a case with an optical drive bay, the Phanteks Enthoo Pro M is excellent (as mentioned by RCFProd).
If you want a case that does have a door, the NZXT H230 is a good option:
http://pcpartpicker.com/part/nzxt-case-cah230ib1
The NZXT S340 that you mentioned is an excellent case that excludes 5.25" bays to save space and clean up the design. With online game distribution systems like Steam, Origin, and the Microsoft Store it really makes sense. You can always use an external USB DVD drive if you ever need one. Windows 10 is even offered with a flash drive maker, so you don't need a DVD drive to install the operating system.
Good luck!