I’d personally recommend broadcasts if you’re happy to pay for the full version. Can’t recall what the limitations are on the free version but I’ve found it worth the price.
The stations you add will also sync accords to your watch, Mac, Apple TV etc. if you have them, and it has a nice and clean iOS / macOS native look & feel.
Listen to streaming internet radio in an ultra-simple, single-purpose app. Broadcasts makes building a library of stations from around the world easier than ever — no subscription required. Use completely free with a limited-size library of stations, or upgrade to the full version to unlock...
apps.apple.com
I’d also recommend checking out
http://www.radiofeeds.co.uk/ , they have links to tonnes of radio streams if there’s anything you can’t find in the default list in Broadcasts.