A Bryton, Lezyne, XOSS or other GPS computer costing under $100 will do what you want.

Just ignore the GPS navigation features. GPS is useful even without navigation aids.

There's one particular sub-$100 Lezyne that needs a USB cable to download data for Strava or whatever the user prefers for privately logging data or publicly sharing rides with friends.

And the XOSS uses GPS only to record routes, but offers no navigation aids whatsoever. However, due to the pandemic, XOSS customer support has been non-existent since February. I bought mine in January. They work fine, although the Android app isn't intuitive and I needed a couple of days to figure out how to sync to Strava. But it's a risky purchase now. Bryton and Lezyne are better bets under $100.