1. What is your neighborhood like? This sounds like it's asking for details of the person's neighborhood - the location, the types of houses and people living there, whether it's more of a suburban or urban area, etc.
2. How is your neighborhood? This is more asking about the well-being of the neighborhood, most likely the homes and people within it. You may ask someone this question if they've recently moved. Maybe you want to know if this person is getting along with their neighbors, if any houses/lots seem run-down, or if there are any recent events that have occurred there.
3. What is the place you live in like? A bit of an awkward sentence - you could reword it as something such as "What is your home like?" or "What is your area like?" depending on how specific you want to be with your question. Similar to #1, this sounds as if it's asking for details, but is also fairly open-ended. You may want to know details about what type of house they have, or maybe what type of area they live in, what type of people live there, etc.
4. What kind of the place do you live in? This is best re-worded as "What kind of place do you live in?" This is asking about the person's home specifically. Do they live in an apartment? A cabin in the middle of the woods? A townhouse at the edge of the city? You're looking to learn about the type of home that this person has.