It honestly just depends on where in the country you want to live and what type of small town you'd enjoy living in. Most all small towns are close knit, that is part of their nature. Many also often have something of an old fashioned mindset, so that is something else that you have to take into consideration when contemplating where to move. I lived in a cute, tiny little town for a while, but the narrow mindedness of the majority of the people was incredibly unattractive to me. Obviously, not all small towns are going to be that way, but in certain parts of the country, you are going to find that to more often be the case. Close knit can also mean that everyone is in your business. If you are a private person at all, this may or may not be what you are looking for.
Small town covers a huge range of sizes as well. Are you looking for a town that still has all the basic amenities such as shopping and groceries (which would actually be on the larger size of "small town"), or are you willing to live farther away from a larger city to get the small town feel, yet still have to do a little driving to get some of those needs taken care of? Where I lived, I didn't have close access to most any shopping, so it was a drive to get anything done. My preference would have been to have had something more convenient, but that would have also meant living farther away from the rest of my family than I was willing to go. It also meant a lot fewer options for employment. Neither of which were issues I was willing to live with to get that small town feel.
To really be able to start looking for what towns are appealing to you, you may need to create a more definite list of what it is you are looking for in a place to live as that will make a huge difference in where you should start looking. There are lots of areas of the country and towns that seem extremely appealing on the surface, but once you look deeper, you may find that the community just doesn't fit your needs or expectations once you see what it would be like to live in it on a daily basis. Until you have defined your own personal needs, like proximity to shopping, availability or quality of employment and education (especially when talking about raising kids), it will be very difficult to even start looking.