How do I JSDoc A Nested Object's Methods?

You can use a combination of @module or @namespace along with @memberof.

define([], function() {

    /**
     * A test module foo
     * @version 1.0
     * @exports mystuff/foo
     * @namespace foo
     */
    var foo = {
        /**
         * A method in first level, just for test
         * @memberof foo
         * @method testFirstLvl
         */
        testFirstLvl: function(msg) {},
        /**
         * Test child object with child namespace
         * @memberof foo
         * @type {object}
         * @namespace foo.bar
         */
        bar: {
            /**
             * A Test Inner method in child namespace
             * @memberof foo.bar
             * @method baz
             */
            baz: function() { /*...*/ }
        },
        /**
         * Test child object without namespace
         * @memberof foo
         * @type {object}
         * @property {method} baz2 A child method as property defination
         */
        bar2: {
            /**
             * A Test Inner method
             * @memberof foo.bar2
             * @method baz2
             */
            baz2: function() { /*...*/ }
        },
        /**
         * Test child object with namespace and property def.
         * @memberof foo
         * @type {object}
         * @namespace foo.bar3
         * @property {method} baz3 A child method as property defination
         */
        bar3: {
            /**
             * A Test Inner method in child namespace
             * @memberof foo.bar3
             * @method baz3
             */
            baz3: function() { /*...*/ }
        },
        /**
         * Test child object
         * @memberof foo
         * @type {object}
         * @property {method} baz4 A child method
         */
        bar4: {
             /**
             * The @alias and @memberof! tags force JSDoc to document the
             * property as `bar4.baz4` (rather than `baz4`) and to be a member of
             * `Data#`. You can link to the property as {@link foo#bar4.baz4}.
             * @alias bar4.baz4
             * @memberof! foo#
             * @method bar4.baz4
             */
            baz4: function() { /*...*/ }
        }
    };

    return foo;
});

EDIT as per Comment: (Single page solution for module)

bar4 without that ugly property table. ie @property removed from bar4.

define([], function() {

    /**
     * A test module foo
     * @version 1.0
     * @exports mystuff/foo
     * @namespace foo
     */
    var foo = {
        /**
         * A method in first level, just for test
         * @memberof foo
         * @method testFirstLvl
         */
        testFirstLvl: function(msg) {},
        /**
         * Test child object
         * @memberof foo
         * @type {object}
         */
        bar4: {
             /**
             * The @alias and @memberof! tags force JSDoc to document the
             * property as `bar4.baz4` (rather than `baz4`) and to be a member of
             * `Data#`. You can link to the property as {@link foo#bar4.baz4}.
             * @alias bar4.baz4
             * @memberof! foo#
             * @method bar4.baz4
             */
            baz4: function() { /*...*/ },
            /**
             * @memberof! for a memeber
             * @alias bar4.test
             * @memberof! foo#
             * @member bar4.test
             */
             test : true
        }
    };

    return foo;
});

References -

1. Another Question about nested namespaces
2. For alternative way of using Namespaces
3. Documenting literal objects

*Note I haven't tried it myself. Please try and share the results.

Here's a simple way to do it:

/**
 * @module mystuff/foo
 * @version 1.0
 */
define([], function() {

/** @lends module:mystuff/foo */
var foo = {
    /**
     * A method in first level, just for test
     */
    testFirstLvl: function(msg) {},
    /**
     * @namespace
     */
    bar4: {
        /**
         * This is the description for baz4.
         */
        baz4: function() { /*...*/ },
        /**
         * This is the description for test.
         */
        test : true
    }
};

return foo;
});

Note that jsdoc can infer the types baz4.baz4 and test without having to say @method and @member.

As far as having jsdoc3 put documentation for classes and namespaces on the same page as the module that defines them, I don't know how to do it.

I've been using jsdoc3 for months, documenting a small library and a large application with it. I prefer to bend to jsdoc3's will in some areas than have to type reams of @-directives to bend it to my will.