mmm a tough one, there are so many!
For strolling along and for scenic points it has to be Newborough, I don't know about the sea for swimming though.
Benllech has a blue flag and is great for the kids, nice sandy beach with an ice cream stand on one side.
Lots of people like Rhosneigr but we nearly got flattened by wind/kite/surfer types the last time we went. Big open beach, lots of space for football.
We stay near Lligwy Bay (just north of Moelfre) which has sand, rock pools, a small river, ice cream van and a private footpath to it from the campsite.
Will that do for now? if I think of anymore I'll let you know
PS We're going camping there next weekend (great big double )