FYI, if you haven't been to SoCal in June before, the beach cities experience a phenomenon called June gloom. This means that it may be chilly and foggy for most of the morning, and then the sun will appear for a few hours in early afternoon, before disappearing again around 3 or 4 pm. You may also get blazing sunshine, but you never know that time of year. Dress in layers, just in case, because it will definitely be cooler than Anaheim. Also, there is a real rush hour on Pacific Coast Hwy (PCH), so the best time to go to the beach is usually between 10-3! I'm a beach addict who lives in Huntington, so here's more info for you, with relative distances from DL...
Laguna - 35-45 min
Pros: The prettiest, hands down. There is a mix of hills, cliffs, and sea, so the scenery is spectacular. It's more upscale, with pricier shops and restaurants, and an artsy, bohemian vibe. There are several waterfront restaurants where you can eat right on the water (Splashes at Surf & Sand is a favorite), or you can pack a lunch. Local secret: If you're up for the drive, head to the Montage Laguna Resort (look at the pics online), use street parking, take the stairs (or the hotel lobby elevator) to access the beach path, and enjoy one of the most stunning views in SoCal. The grounds are immaculate with cliffside ocean views from paved walkways, and there are gorgeous public beaches on the property. Our favorite, called Treasure Cove, is harder to access - down a steep path or a lot of stairs - but it has awesome tide pools. But don't eat at the Montage unless you want to drop serious cash. LOL.
Cons: Laguna is further south, and traffic can build up because it's more secluded.
Huntington - 25-30 min
Pros: Surf City, USA. This is the beach most people think of when they think of Orange County, with palm trees, big waves, surfers, street performers, and people walking around everywhere in swimsuits. It's very laid-back, and the beach path stretches for miles. It has a great pier, and in addition to the restaurants and bars on Main Street, there's a more upscale open-air mall, Pacific City, right across from the beach with a variety of eateries. We like Simmzy's or Bear Flag Fish Co., but there are several options to suit your taste, and the food court is very fun to explore (custom popsicles, a beef jerky bar, etc).
Cons: It gets crowded (especially around Main street), but it's such a big beach that there is ample parking, especially if you head away from the pier.
Crystal Cove - 30 min
Pros: Barely developed, and gorgeous. It's a state park. If you only want to hang out on the beach, and not walk around a downtown/village area, this may be your best bet.
Cons: Limited dining options, and the entrance fee is $15 per car.
Newport - 25-30 min
Pros: Big waves on the beach, and lovely calm views in the harbors. You can visit Newport Beach, the Balboa Peninsula, the Balboa Fun Zone (if you have kids), and take the car ferry across the harbor at the end of your visit.
Cons: Parking can be horrendous in the summer, and since Newport is one of the most expensive areas in SoCal, most shops and restaurants are outrageous.