Return an object from a function that has nested ajax calls

Yes, you should use deferred objects.

The simplest approach here is to create an array into which you can store the jqXHR result of your inner $.getJSON() calls.

var def = [];
for (var i = 0; ...) {
    def[i] = $.getJSON(...).done(function(videoDetails) {
        ... // extract and store in youtubeMap
    });
}

and then at the end of the whole function, use $.when to create a new promise that will be resolved only when all of the inner calls have finished:

return $.when.apply($, def).then(function() {
    return youtubeMap;
});

and then use .done to handle the result from your function:

getYoutubeDurationMap(query).done(function(map) {
    // map contains your results
});

See http://jsfiddle.net/alnitak/8XQ4H/ for a demonstration using this YouTube API of how deferred objects allow you to completely separate the AJAX calls from the subsequent data processing for your "duration search".

The code is a little long, but reproduced here too. However whilst the code is longer than you might expect note that the generic functions herein are now reusable for any calls you might want to make to the YouTube API.

// generic search - some of the fields could be parameterised
function youtubeSearch(query) {
    var url = 'https://gdata.youtube.com/feeds/api/videos';
    return $.getJSON(url, {
        q: query,
        'max-results': 20,
        duration: 'long', category: 'film',  // parameters?
        alt: 'json', v: 2
    });
}

// get details for one YouTube vid
function youtubeDetails(id) {
    var url = 'https://gdata.youtube.com/feeds/api/videos/' + id;
    return $.getJSON(url, {
        alt: 'json', v: 2
    });
}

// get the details for *all* the vids returned by a search
function youtubeResultDetails(result) {
    var details = [];

    var def = result.feed.entry.map(function(entry, i) {
        var id = entry.id.$t.substring(27);
        return youtubeDetails(id).done(function(data) {
            details[i] = data;
        });
    });

    return $.when.apply($, def).then(function() {
        return details;
    });
}

// use deferred composition to do a search and then get all details
function youtubeSearchDetails(query) {
   return youtubeSearch(query).then(youtubeResultDetails);
}

// this code (and _only_ this code) specific to your requirement to
// return an array of {id, duration}
function youtubeDetailsToDurationMap(details) {
    return details.map(function(detail) {
        return {
            id: detail.entry.id.$t.substring(27),
            duration: detail.entry.media$group.media$content[0].duration
        }
    });
}

// and calling it all together
youtubeSearchDetails("after earth").then(youtubeDetailsToDurationMap).done(function(map) {
    // use map[i].id and .duration
});