Even though you originally asked about radios it sounds like a Blue Tooth speaker is more in line to what your wanting if a built in am/fm tuner isn't necessity as you mention further along in the original post.
I have a few different ones and use them often with a tiny MP3 player that also has AM/FM and SDS sound card options. Of course you can use smartphone Ipod etc that does all that too
Plenty of options in BT for size, and/or sound quality, plus numerous ones have an IP water resistance rating for outdoor use, some even be submerged in water and still work, and many have rubberized boot protection.
Some including the Altec Lansing I have also has threaded insert for a more permanent mounting with a bolt. Though hook and loop or two sided 3m tape could be options too.
I have quite a few outdoor/worksite options for sound and the Milwaukee M12 radio was the very first, it's one rugged radio. And I have an inexpensive BT receiver adapter on it too so I can also wirelessly stream to it. And that was followed by the small Milwaukee wedged shaped BT speaker. I have carabineer clipped to that for a secure attachment for like on a tool bag. Again its built tough.
Since then purchased the new dual battery BT speaker Milwaukee released awesome sound and pretty bulletproof but you really pay for it too.
I also have Sunex Tools socket speaker it looks like impact socket

and it has a fairly secure magnetic base for flat metal surfaces like a tool box, fender or even the ROPS. Holds pretty good though normally I won't be driving around with it like that!
Battery life maybe important and many with built in rechargeable batteries have different run times and recharge times. This is probably the main reason I like the power tool battery sound options I can quickly swap out batteries if needed but what BT speakers I have has pretty phenomenal runtime and easily more than all day long. Radio pulls more power from the batteries but still good too.
Amazon is full of speaker options. Prices vary from < $20 range to over $100 and of course sound quality and loudness will too. I have also seen dual wireless BT speakers offerings recently.
There is an older thread on few different BT speakers and some worksite radios
http://www.tractorbynet.com/forums/attachments/348910-bluetooth-speaker-tractor-recommendations.html
Let us know what you end up with