After six trips to Mykonos, I have to confess I've only done one side of the island. That's because my favorite beach is Super Paradise Beach, where I always go. However, on the way to Super Paradise, which is a bit remote, there are three other beaches. The first is Plati Yialos. It's mainly a family beach for package tourists. It's very pleasant, actually, without the loud music that blares on the other beaches and with lots of places to eat.
The next beach to the east is a small beach called Paranga, which used to consist of a small shack and a few beach chairs. Now it's connected to Mykonos Camping and is a full-on sunning and dancing extravaganza.
Next is Paradise Beach, which also has a campground with a restaurant, shop, and four bars. It's definitely the place to be if you're young, straight, and want to party. There are also sports in the water (I don't want to say water sports) if you want to do something athletic. I usually bypass it, of course, and hike onto Super Paradise (though they have a market at the bus station that has the cheapest prices on the island!).
For those not as adventurous, you can take the bus to Plati Yialos or Paradise and then a small boat to Super Paradise. No buses to go SP. If you have your own car, you can get to SP, but the roads may be a bit difficult to navigate. Anyhow, despite being somewhat remote, Super Paradise is usually packed. Three quarters of it is straight and the rest is gay, tucked in the western corner. On the straight side, there's a reasonably-priced cafeteria and a loud bar, perfect for drinking and dancing, though this starts in the mid-afternoon. On the gay side, there's the Coco Club, which overlooks the beach and water and has table surrounding a pool. It's very pleasant and the food is good.
There's plenty of eye candy, no matter what you're looking at, but it's not intimidating because there are people of all shapes, sizes, races, and ages there. The weather varies from day to day, as sometimes it's perfect, sometimes, too hot, sometimes too windy. But if it doesn't seem pleasant to go to the beach, you can always catch a ferry to Delos or just stay in town and shop and sip coffee.
There's another beach beyond here called Elia, but I've never been, though many people say they prefer it because it's less crowded.