Always lots of stuff to do in OC, especially in the summer.
In June you may run across lots of high school grads, so the crowd may be a but rowdier, but not out of control. Prices are also lower in June than the peak July season.
June 10-11 is the air show weekend. This is a spectacular, fun event that take place over the ocean at the south end of town. You ca see it for free from lots of places, or buy tickets for an even better view. More info at:
http://www.ocairshow.com/Home.html Some great places to stay include Spinnaker (ocean block, right of the boardwalk), Flamingo (ocean block, just north of the boardwalk), Castle in the Sand (ocean front), Dunes Motel or Dunes Manor (both ocean front, just north of the boardwalk), Holiday Inn (either on the BW or at 67th Street, both ocean front).
Some of my favorite places to eat seafood are Captains Galley (West OC), Marina Deck (Dorchester Street on the Bay), Bahama Mamas (great crabs, Wicomico Street on the Bay), Harrison's Harbor Watch (at the inlet, great views). For more casual dining try Harborside in West OC, one of my favorite places. For a romantic dinner you can't go wrong with the spectacular sunset views and great food that both Fager's Island and The Hobbit have to offer. Smokers BBQ (west OC or Rt 611) had great BBQ and JRs has excellent ribs. Also having a crab feast can be great fun. I recommend getting a dozen or so big crabs rather than all you can eat, because I'd rather pick bigger crabs, and the cost difference is not that much, but AYCE can be fun too.
Fun things to do include spending time on the great beach, strolling (or renting a bike and riding on) the boardwalk, eating great vacation food including Thrasher's Fries, Fisher's Popcorn, or Dumser's Ice Cream. Go carts in West OC , Trimper's Rides, Jolly Roger, and the many arcades also can be great fun. The Beach Plaza Hotel has a piano bar that can be great fun. OC also has lots of great golf, from mini golf, to short courses, to pro-level courses. From the first time golfer to the great golfer there is a nearby course where you can have fun. There are also tons of fun things to do on the bay, including renting jet skis, para sailing, renting boats, crabbing, and fishing.
I'm sure others will add more excellent ideas. Have a great trip!