Move router downstairs...

Not sure if this is the right place to post this and this may be a dumb question, but i have three coax outlets to plug in my tvs and router into in the house. The router is upstairs and always has been. However i want to move it into the living room. It it more centrally located. I can put a splitter on the coax and connect both the router and the DVR to it and get internet connectivity/cable right? Or is there a designated outlet that the router must be plugged into?