People here are using different terminology than I am used to, but it sounds to me like you can move the modem to a new place and the usual setup is then modem to router to switch, with CAT-6 cable running hard wired from the switch to your preferred places. Cat6 cables or higher can allow power over ethernet (POE) which is "a technology for delivering DC power to devices over copper Ethernet cabling, without separate power supplies or outlets." (from Cisco). These wires can terminate in mini switches to allow for a media center (I have runs to three such places) as well as to a computer, a storage system like a Synology NAS, and to WIFI devices to allow you to create a much more reliable Wi-Fi network than using a Wi-Fi/router combination, with other areas only being connected to the router via Wi-Fi.
The primary advantage of moving the modem-router-switch (and the NAS) to one place is that they create noise and heat and require some degree of ventilation, so coming into an area where you listen to music is not so cool IMHO. If you have other stuff like a home security NVR then that too should be hidden away.
The PoE Cat 6 runs to your listening areas can then be plugged directly into those things you have that need that ethernet, and those are going to perform far better than anything connected via Wi-Fi.