I used a sigma bc 16.12 in all weatger with no issue. It did have cadence but I believe they have a model that comes without those sensors. It did have a backlight however, the backlight wouldn't stay on for longer than say 10 seconds.

Also, the head unit would lose its signal to the wheel speed sensor from my bike headlight - I guess the LEDs produced rf interference and would block the signal.

I've upgraded to a lezyne super GPS. I know that's out of your price range however, it's waterproof, has a backlight that stays on, is unaffected by my headlight and it's user interface with your phone and synching to strava (if this interests you) is very intuitive.

As more of a commuter than leisure rider - I've come to appreciate how durable it is and how long the batter life is (24 hours).

They have other models that may be closer to your price range but if I remember correctly, they're all more expensive than 80 bucks USD.