The problem is not the JSONArray.toString(), as @Selvin mentioned.

From JSONArray source:

/**
 * Encodes this array as a compact JSON string, such as:
 * <pre>[94043,90210]</pre>
 */
@Override public String toString() {
    try {
        JSONStringer stringer = new JSONStringer();
        writeTo(stringer);
        return stringer.toString();
    } catch (JSONException e) {
        return null;
    }
}

/**
 * Encodes this array as a human readable JSON string for debugging, such
 * as:
 * <pre>
 * [
 *     94043,
 *     90210
 * ]</pre>
 *
 * @param indentSpaces the number of spaces to indent for each level of
 *     nesting.
 */
public String toString(int indentSpaces) throws JSONException {
    JSONStringer stringer = new JSONStringer(indentSpaces);
    writeTo(stringer);
    return stringer.toString();
}

The problem is that you need to convert your ChecklistAnswer to JSON object first for your JSONArray to work properly.

Again from Javadoc:

/**
 * A dense indexed sequence of values. Values may be any mix of
 * {@link JSONObject JSONObjects}, other {@link JSONArray JSONArrays}, Strings,
 * Booleans, Integers, Longs, Doubles, {@code null} or {@link JSONObject#NULL}.
 * Values may not be {@link Double#isNaN() NaNs}, {@link Double#isInfinite()
 * infinities}, or of any type not listed here.

...

Take a look at this tutorial. Also you can parse above json like :

JSONArray arr = new JSONArray(yourJSONresponse);
List<String> list = new ArrayList<String>();
for(int i = 0; i < arr.length(); i++){
    list.add(arr.getJSONObject(i).getString("name"));
}

As long as it's a valid JSONArray to begin with, then yes.

Use gson. It's got a much friendlier API than org.json.

Collections Examples (from the User Guide):

Gson gson = new Gson();
Collection<Integer> ints = Lists.immutableList(1,2,3,4,5);

//(Serialization)
String json = gson.toJson(ints); ==> json is [1,2,3,4,5]

//(Deserialization)
Type collectionType = new TypeToken<Collection<Integer>>(){}.getType();
Collection<Integer> ints2 = gson.fromJson(json, collectionType);
//ints2 is same as ints

Nikita already gave you the correct solution, but here it is, step by step.

I reduced your problem to this minimal test:

import com.google.gson.Gson;

public class TestGSON 
{
    public static void main( String[] args )
    {
        // that's your JSON sample
        String json = "[{\"reserve_no\":\"20\",\"city\":\"city2\",\"street\":\"street1234\",\"discription\":\"discription123\",\"date\":\"2012-10-22 04:47:54\",\"customer\":\"abc\"}]";
        // note: we tell Gson to expect an **array** of Data
        Data data[] = new Gson().fromJson(json, Data[].class);
        System.out.println(data[0]);
    }
}

The problem is that your JSON fragment is actually an array of objects, not just an object (hence the [] around it). So, you need to tell GSon it must expect an array of Data, not just a Data object. By the way, the exception that's thrown when executing your code as-is already told you so:

Exception in thread "main" com.google.gson.JsonSyntaxException: java.lang.IllegalStateException: Expected BEGIN_OBJECT but was BEGIN_ARRAY at line 1 column 2

unless of course it got swallowed by an empty catch block

With respect to the Data class: think twice before you override the toString method like you did here. I would drop that method and just do

System.out.println( data[0].getCity() );