Having lived in SC all my life, I can voice an opinion. Aiken is a small town, and does have a history of having horse farms. But I would suggest Greenville in the upstate. If is much more progressive, and has a lot more to offer than Aiken. It's larger, but still has the small town atmosphere. It is surrounded by rural areas and land is cheap. It is on the I 85 corridor between Atlanta and Charlotte. It is the home of BMW and Michelin's US corporate headquarters so it has a strong economy and a culture more international and diverse than Aiken. It has an incredible downtown with great restaurants, theaters, art and many cultural events. It is near the mountains, close to Asheville NC and also Tryon, which is an much more an equestrian town than Aiken. They are developing a huge equestrian center in Tryon. It's about 30 minutes from Greenville. Historic Charlestown is three hours away and SC has great beaches like Kiawah and Hilton Head. The blue ridge mountains are visible from Greenville. Greenville has won many awards for its phenomenal revitalization.
I think you would find Aiken a little too "old South" whereas Greenville has much more diversity and is welcoming . As far as crime, it's a very safe city with little poverty and a very vibrant downtown. I often walk there from my home which is over a mile away. I also own a several hundred acres nearby where I go play.
I would visit downtown. Stay at the Westin Poinsett and walk around and dine. Then visit northern Greenville county which is at the foothills of the mountains and quite beautiful. Look at the area around Furman university. Avoid the eastern "suburbs" where most newcomers move to as the traffic is worse and it is mostly shopping and bustling retail.
Like many areas of the south, there is an element of lesser educated people but still decent people. Religion is big here, but not required. But unlike most Southern cities, Greenville had progressed from the influx of diverse people, brought here by the industries like Michelin and BMW. So its the new South. Still has the friendliness of southern culture, but growing more sophisticated. Cycling is huge here. George Hincappie, the most famous American cyclist (other than Lance Armstrong) lives here either his French wife. We hosted the US National cycling championships the last few years. When I cycle on the beautiful rural roads north of here, I have seen Hincappie and Armstrong and other international teams training here. We also have a Red Soxs minor league baseball franchise and a cool downtown stadium and also a pro ice hockey team. and Clemson University is nearby.
Tell me more what you are looking for and what you require, and I will be glad to offer my opinion. But In my opinion, Aiken is not that special. It's economy suffered from jobs lost from the downsizing of the savannah river nuclear facility over the last few decades and there's just not a lot there that's appealing to me.
If you are considering SC, Greenville wins easily.