I would be surprised if you could find a rental car on the island 
...
That being said, if you could find a car (or if the resort has bicycles available), you could probably entertain yourself for a day exploring the island! It is quite flat and would be fun to explore by bike, though bikes hadn't really been introduced when I was there. We did have access to cars at the school, but also did a lot of walking... Sailrock had just finished building their first few private homes and East Bay Resort was not yet completed and operational when I left (even though the structure had existed for many years after it was pretty much abandoned by the first owners). I heard that East Bay had brought a bunch of bikes to the island, but I can't confirm that... Google seems to think there's a bicycle rental shop in town now too though so that's probably right.
The town is about a 15-20 minute walk from East Bay. There aren't really any main attractions per say, but the only town (Cockburn Harbour) has some historic buildings that are interesting to see. We worked with Sailrock to research and create informational materials on the history of these buildings, so there might be signage around town by now? Regardless, people were very friendly to visitors and you could also swing by the docks and watch the fishermen come in with conch and lobster if you wanted. If you're feeling a bit more adventurous, there are a few small establishments that served food. Cracked conch was a favorite from the place right by the harbor (looks like it's called Sunset Cafe now), and there's a guy who served jerk chicken and pork on Friday and Saturday nights that I can't recommend enough (looks like it's called Triple J Grill now)! Seriously, his food is probably one of the things I miss the most...
The SE corner of the island has essentially no development and some really nice remote beaches, but might be a little far to walk to. At one point there was also a historic house (previously the Governor's residence?) out on the SE corner, but this may have been destroyed by a hurricane. We would often head out there on our days off to visit these beaches and generally explore the island. If you were really ambitious, you could even try to make it up to Bell Sound or to the Northern tip of the island where the ruins of the old US Coast Guard Station are located. There is some nice snorkeling up in the channel between South Caicos and East Caicos and Bell Sound is popular for bone fishing.
The entire center portion of the island is a salina (salty marsh), and does have excellent birdwatching if that's your thing. This is very close to East Bay. Because it was previously developed to harvest salt, there are a lot of stone walls you can walk on into the ponds. I helped a group that was writing a bird watching guide while I was there, so if this is something you're interested in I can try to find it and send you more information on that.
Hope that helps!
... That being said, if you could find a car (or if the resort has bicycles available), you could probably entertain yourself for a day exploring the island! It is quite flat and would be fun to explore by bike, though bikes hadn't really been introduced when I was there. We did have access to cars at the school, but also did a lot of walking... Sailrock had just finished building their first few private homes and East Bay Resort was not yet completed and operational when I left (even though the structure had existed for many years after it was pretty much abandoned by the first owners). I heard that East Bay had brought a bunch of bikes to the island, but I can't confirm that... Google seems to think there's a bicycle rental shop in town now too though so that's probably right.
The town is about a 15-20 minute walk from East Bay. There aren't really any main attractions per say, but the only town (Cockburn Harbour) has some historic buildings that are interesting to see. We worked with Sailrock to research and create informational materials on the history of these buildings, so there might be signage around town by now? Regardless, people were very friendly to visitors and you could also swing by the docks and watch the fishermen come in with conch and lobster if you wanted. If you're feeling a bit more adventurous, there are a few small establishments that served food. Cracked conch was a favorite from the place right by the harbor (looks like it's called Sunset Cafe now), and there's a guy who served jerk chicken and pork on Friday and Saturday nights that I can't recommend enough (looks like it's called Triple J Grill now)! Seriously, his food is probably one of the things I miss the most...
The SE corner of the island has essentially no development and some really nice remote beaches, but might be a little far to walk to. At one point there was also a historic house (previously the Governor's residence?) out on the SE corner, but this may have been destroyed by a hurricane. We would often head out there on our days off to visit these beaches and generally explore the island. If you were really ambitious, you could even try to make it up to Bell Sound or to the Northern tip of the island where the ruins of the old US Coast Guard Station are located. There is some nice snorkeling up in the channel between South Caicos and East Caicos and Bell Sound is popular for bone fishing.
The entire center portion of the island is a salina (salty marsh), and does have excellent birdwatching if that's your thing. This is very close to East Bay. Because it was previously developed to harvest salt, there are a lot of stone walls you can walk on into the ponds. I helped a group that was writing a bird watching guide while I was there, so if this is something you're interested in I can try to find it and send you more information on that.
Hope that helps!
