These are located together in front of the Eden Rock dive shop in downtown George Town. These both have several cool swim throughs and are fairly swallow (15' to 45'). As there are many people doing these dives, it would probably be pretty easy to hook up with a dive buddy at the dive shop. They also offer guided night dives once or twice a week, so this would fairly cheap (as far as Cayman goes)
There is also the wreck of the Cali a little to the north in downtown. The wreck is all busted up so there is no penetration, but there are lots of fish and critters, with some nice coral heads just to the south all at about 25'. This is in front of Don Fosters main shop, but I heard they recently moved, so I don't know if there is another dive operator there so you may have more difficulty rounding up a buddy on site.
Just South of downtown, the Sunset House has a decent house reef with the statue of Aphrodite. Up on the north end of the island by the Turtle farms in front of Dive Tech is a mini wall. Both of these sites should have plenty of divers around to glom on to another group or pick up a buddy.