Where can I back up my photos if I don't want to pay for Google Photos?

Google Photos gives you 15 GB free and that's plenty if you compress the images, but if you want something free with no limits you've got options like Nextcloud (which you install on your own server or cheap hosting), Synology if you have a NAS, or just connect your phone to a computer and make copies on an external hard drive, which is the simplest. Some people also use Amazon Photos which comes with Prime, or Flickr which offers 1 TB free with no ads. The important thing is that you make backups in more than one place, because trusting everything to a single platform is risky.