If you’re on Apple products, go get NetNewsWire in the App Store and use your iCloud space to sync subscriptions between devices. You’ll have to manually add RSS feeds, but those are usually discoverable by doing a web search for your site + feed or rss, or by adding /feed or /rss to the end of the site URL to see if it’s hiding there.
Most websites that have RSS have a meta tag that identifies the RSS feed, you can just put the normal URL to the site/blog into your RSS reader and it will pick up the RSS feed URL from the meta tag.
