A great way to see the city is in a horse-drawn carraige. Or maybe you can rent bikes. Walking would probably be a bit much if you really want to see a lot of houses, and if you drive you won't be able to take in the sights.
Carleston is a beautiful city, I hope you enjoy it!
There are several horse-drawn tours of the city, but i believe their "range" is limited. Unfortunately, their largest touring (trolley type tours) company "packed it in" a couple of months ago. If you're only there for a short time, you really need the services of a guided tour. The busiest area of town is called the Marketplace in old town.