That way a computer would be up and running all the time. Not an ideal situation really, at least for me.Isn't it possible to configure a new network using a computer in your "Computer room"? and plug your NAS into your computer directly.
Yeah thats one way to go about it but Synology has fixed list of Wireless adapters it supports.Theoretically, you should be able to connect your NAS to Wifi router by connecting a Wireless Network Adapter to your NAS USB Port. I am not sure if your NAS supports it.
Synology NAS supports plugging USB wireless dongle. Verified this here
I think I am gonna go ahead using the wireless repeater solution. Lets see