I work at Tortuga Divers at Morritt's Tortuga Club. Let me try to make my comments a bit general to East End diving.
Morritt's Tortuga Club and The Royal Reef are the two large resorts on the East End of Grand Cayman. These resorts are on adjoing properties on the northeast tip of the island in what is technically Colliers. Colliers is so tiny that it doesn't even qualify as a village. Almost all of the other resorts are along Seven Mile Beach on the other end of the island.
Both properties are located on a very quiet stretch of uncrowded beach. Even in the busiest time you have plenty of room to spread out. Both resorts provide plenty of beach lounge chairs.
Diving East End is with one of three operators - Tortuga Divers (at Morritt's), Ocean Frontiers (stand alone shop in Sand Bluff plus a retail only shop at The Royal Reef) or Cayman Diving Lodge (in East End village). All of the operators take advantage of numerous buoys marking all of the popular East End dive sites. Each shop also has a few secret spots for anchor drops.
East End offers wall diving along the sheer drop of the Cayman Wall (which circles the island). Some sites have sand chutes with canyonways or tunnels heading out onto the wall. The wall is much steeper on East End than on the west side.
Many shallow sites are along a mini-wall drop off. Some of those sites are deeply eroded with numerous coral heads broken away from the mini-wall. Swim thrus, canyonways, and a few caverns dot these sites.
Generally, the coral is healthier on East End due to less diver pressure. We have beautiful reefs with vibrant soft and hard corals. So you have realistic expectations, we do not have: wrecks, wall sites shallower than about 50ft, or consistently flat calm seas.
Tortuga Divers often handles newly certified divers. We require new divers to stay shallow (max 60ft) while they build experience.
As to other considerations, it may be rather hot in July with less wind (and perhaps calmer seas). I haven't looked at a calendar, but Spring Break is a very busy season especially Easter week. Between those dates we would expect thimble jellyfish season to come and go.