My family has been to Cayman many times and we (interestingly enough) will be on the island in early July ourselves.
We have never stayed anywhere other than 7 mile beach, but I have heard that the south sound is nice.
As far as activities, the big hitters are:
1) Stingray City sand bar. Usually the companies that take you out have boats that will take you snorkeling in a few places in addition to Sting Ray city
2) Snorkeling. I am not familiar with the snorkeling in the south sound area (I am sure there is good snorkeling there I just havnt ever been). There is an EXCELLENT snorkeling spot on 7 mile beach just out from the cemetery. You don't have to swim more than 20 or so yards from shore.
3) Diving. Cayman usually gets rated as a top 2 or 3 dive spot in the carribean. If you have any desire to dive, I would do it on this trip. Most dives are 2 tank dives where the first dive is "off the wall". Just off the shore (easily less than a mile in many places) the sea floor drops off from ~100 feet into the Cayman trench at a few thousand feet. It does so in the form of a nearly vertical wall. It is an amazing site to see. The most dramatic drop offs are on the north wall, but due to currents, most of the diving in July is off of the west wall (west side of the island), directly out from 7 mile beach.
4) Water sports. Lots of companies will rent you jet skis, kayaks, etc. There are tons of opportunities for parasailing and other motor sports of the sort.
As far as restaurants there are a lot of good ones.
1) The best is probably Casanovas which is an Italian restaurant in Georgtown that is right on the water. Not cheap, but reasonably priced in my book.
2) Deckers is a bit more upscale but good food. Although, I think it is a bit over priced.
3) Coconut Joes is a laid back restaurant that has a good variety for pretty cheap
4) Lone Star is another casual place that has a good reasonably priced selection. Apparently it used to be owned by an Aggie but has since been sold.
5) Eats caf is another reasonably priced casual place.
6) Chicken Chicken is a lunch type fast food spot but really good and worth a trip if you've never had it.
7) Calico Jacks is an (in my book) AWESOME beach bar. It is on the public beach on 7 mile beach and is a stereotypical Caribbean beach bar. Definitely worth a visit.
Finally, just a heads up. If you are planning on visiting a grocery store for food/drinks/etc, make sure to stock up on SATURDAY. Virtually the entire island (including the grocery stores) shuts down on sunday. So if you need something, get it Saturday.