For travel and biking, I use Shockz headphones. They’re not noise‑canceling, quite the opposite in fact.
This is crucial when riding a bike so you can hear traffic or even walking through the bus/train stations so you can hear the announcements – while still enjoying music or podcasts etc. The battery life is decent, though not as long as my Sony WC100 Bluetooth headset. No cables to get caught up in.
I also have the Sony WC100 for when I am pottering around the garden or on flights because it blocks out airplane noise reasonably effectively and has excellent battery life.
Each of these headsets serves its purpose: Shockz for outdoor safety, Sony for blocking out some background noise without active noise cancelling and longer battery life.