The clever stuff in Time Machine happens on the client and not on the Time Capsule so you can do Time Machine backups to any wi-fi available hard drive. If you have a computer that's always on you can attach and share an external hard drive from it.
At home I have an external hard drive attached to a Mac Mini which backs up the Mac Mini locally and iMac and Macbook via wi-fi.
You could also buy a dedicated NAS unit. I use both QNAP and Synology units as Time Machine destinations. These would give you much more flexibility than a hard drive just hanging off a router.
You can also do a home build NAS server using a Raspberry Pi
Alternatively, you could just go for the simple router with USB port. I haven't tried this option yet as I've not needed to.