Is there a built-in method for selecting closest n siblings

There's no built in method to do this, but it's easily done without using if/else:

$(document).on("click", "#footer button", function () {
    var that = $(this),
        index = that.index(),
        prev = that.prevAll('button:lt(4)'),
        next = that.nextAll('button:lt(4)');
    that.siblings().removeClass('highlight');
    that.add(prev).add(next).addClass('highlight');
});

JS Fiddle demo.

Incidentally, a simple plugin could be easily created/used:

(function($){
    $.fn.rangedHighlight = function(range,highlight) {
        var that = this,
            prev = that.prevAll().slice(0,range),
            next = that.nextAll().slice(0,range);
        that.siblings().addBack().removeClass(highlight);
        that.add(prev).add(next).addClass(highlight);
        return this;
    };
})(jQuery);

$('#footer').on('click', 'button', function(){
    $(this).rangedHighlight(4,'highlight');
});

JS Fiddle demo.

Unfortunately I hadn't noticed, until it was pointed out in the comments, the necessity of always highlighting the full specified range of elements, even if that offsets the clicked element from the centre of the highlighted section. There doesn't seem to be any way of doing this without using an if/else of some sort (though I'm trying to simplify it).

While the above remains true (there is no built-in method), I did decide to rewrite the plugin to offer the choice to do so (in case it's of any use to you):

(function($){
    $.fn.rangedHighlight = function(opts) {
        var that = this,
            index = that.index(),
            s = $.extend({
                'range' : 9,
                'highlight' : 'highlight',
                'highlightClicked' : false,
                'alwaysShowFull' : true,
                'returnRange' : false
            }, opts),
            eitherSide = Math.floor(s.range - 1)/2,
            all = that.parent().children(),
            leftLimited = index < eitherSide,
            rightLimited = index > all.length - eitherSide - 1,
            rangeMin, rangeMax, returnObject;

        that.addClass(s.highlightClicked, 'string' === typeof s.highlightClicked);

        if (!leftLimited && !rightLimited) {
            rangeMin = index - eitherSide;
            rangeMax = index + eitherSide + 1;
        }
        else if (s.alwaysShowFull && (leftLimited || rightLimited)) {
                rangeMin = leftLimited ? 0 : all.length - s.range;
                rangeMax = leftLimited ? s.range : all.length;
        }
        else if (!s.alwaysShowFull && (leftLimited || rightLimited)) {
                rangeMin = leftLimited ? 0 : index - eitherSide;
            rangeMax = leftLimited ? index + eitherSide + 1 : all.length;
        }

        that.siblings('.' + s.highlight).removeClass(s.highlight);
        all.slice(rangeMin, rangeMax).addClass(s.highlight);

        returnObject = s.returnRange === false ? this : all.slice(rangeMin,rangeMax);

        return returnObject;
    };
})(jQuery);

$('#footer').on('click', 'button', function(){
    $(this).rangedHighlight({
        // Number: number of elements _in total_ to be highlighted:
        'range' : 7,
        // String: the class-name to be applied to selected elements:
        'highlight' : 'highlight',
        // Boolean: shows the full range even if that range 'overlaps'
        // the start/end points:
        'alwaysShowFull' : true,
        // Boolean: return the selected range (true) or the clicked
        // element (true), for chaining purposes:
        'returnRange' : false,
        // String: specific class to add to the clicked element:
        'highlightClicked' : false,
    });
});

JS Fiddle demo.

References:

• JavaScript:
  • Conditional ('ternary') operator (condition ? conditionIsTrue : conditionIsFalse).
  • Math.floor().
  • typeof.
• jQuery:
  • add().
  • addBack().
  • addClass().
  • children().
  • index().
  • Greater-than (:gt()) selector.
  • Less-than (:lt()) selector.
  • nextAll().
  • on().
  • parent().
  • prevAll().
  • removeClass().
  • siblings().
  • slice().