Finding image by date
Try something like this:

if (now.getTime() &lt; boise.date.getTime() ) {
    banner.attr('src', imgDir+boise.img+'.jpg');
}
.....


In total,

var now = new Date();
    objs = { 
        // here I change your 12 variables to a single object, so I can loop over them
        boise : { date: new Date ('May 15, 2012'), img: 'Boise' },
        central : { date: new Date ('May 21, 2012'), img: 'Central' },
        notreDame : { date: new Date ('May 27, 2012'), img: 'NotreDame' }
    },
    banner = $('#nextGameBanner'),
    imgDir = 'images/nextGame';

// making loop with objs

$.each(objs, function(key, singleObj) { 
   // compare time with now and stored time in object
   if (now.getTime() &lt; singleObj.date.getTime() ) {
     // assigning src to image when the condition satisfied
     banner.attr('src', imgDir+ singleObj.img +'.jpg');
     break; // stop the loop when match found
   }
});


​
read about getTime()