Bucuti is a beautiful small resort in the low rise area. It's perfect for your honeymoon - quiet, romantic

with very few kids and is on the most beautiful expansive beach!
While there is little night life within walking distance, there are some good restaurants you can walk to...and the downtown and the high rise areas are a quick taxi ride away. You can also use the local bus, which is very inexpensive.
That being said, a car rental for at least a day or two is a great idea so you can explore the rest of the island. Each year we go, we now rent a car for our entire stay so we can up and go on a whim whenever we feel like it.
I think you will love Bucuti - enjoy your honeymoon. Congratulations!