Lesbos - Mitilini for 1 day advice

I'm traveling to Lesbos with my family and will only be there for one afternoon. We arrive into Mytilini Port at 9am and depart at 4pm. I really want to spend the day at a beach on loungers. It looks like the closest beach club is the Bracciera Beach Bar, but research shows that Anaxos beach might be the better option (less rocky, etc), though it's further away. Specifically just want to go in the ocean, have lunch, and lay in the sun.

Can anyone speak to either beach? Are there taxis or buses readily available, or is that something I might have to book in advance? Any recommended beach clubs?

Thanks for your help!