As long as your router has a cable modem in it you can pretty much put it where you want.
You need to be very careful exactly how many splitters and where you place them. Pretty much for maximum performance you want to split the signal one time with a 1x2 splitter where it enters the house, one for your router and one for the TV. You can then split the TV side more times with more splitters. Other arrangements work but you will degrade your network speed in some cases.
Now if what you want to do is run your LAN between multiple pc in your house over the coax cable you will need special devices called "moca" that allow you to do this.