I've personally never tried to split the HDMI output from a Nextbox to another set. Maybe someone in the Community could help you out with your inquiry? @OLDYELLR@Gdkitty@Datalink feel free to chime in .
Re: Using HDMI splitter after output from HD Nextbox
An HDMI splitter should work, however, some inexpensive ones have been problematical due to signal loss or poor quality. The only way to know for sure is to try it, perhaps purchasing it from a store with a good return policy.
In addition, the cables for connecting to/from the splitter need to be appropriate. Cables longer than about 10' need be of a thicker gauge (say 24 or 22 ga) to ensure a good signal, or perhaps utilize RedMere technology if you're attempting to go 25' or more.
You may be able to purchase a used HD STB for about the same money and then be able to watch different programming on each TV.