The instance initialiser is just syntactic sugar in this case, right? I don't see why you need an extra anonymous class just to initialize. And it won't work if the class being created is final.

You can create an immutable map using a static initialiser too:

public class Test {
    private static final Map<Integer, String> myMap;
    static {
        Map<Integer, String> aMap = ....;
        aMap.put(1, "one");
        aMap.put(2, "two");
        myMap = Collections.unmodifiableMap(aMap);