Agreeing with /u/CommodoreCoCo there. Generally speaking, as a graduate student, my advice for finding graduate programs is to read widely, figure out whose work you like and find interesting, then figure out where those people teach. Although I'm at a UK institution and so our graduate programs are generally faster than a lot of American ones (one year for a standalone master's and three for a PhD), your relationship with your thesis advisor is going to be one of, if not the most important relationship of your early academic career. It's an advisor's job not only to help guide your research but also to help you gain visibility in the professional academic world through pushing you to publish, give conference talks, etc., and also by introducing you to others in their network within the field. Of course, if your program requires some taught components as well as the independent research aspect, then you're going to want to find a program that offers a fair number of relevant courses in your subject. That said, generally speaking, if you find a good advisor candidate somewhere, it's very likely that that school will offer the necessary courses as well.
Sorry if that's not particularly helpful...the other thing to do would be to check out the QS and Higher Ed university subject rankings to find which univerities' history programs are ranked highly in general and then from there do some investigation on the department's website to see what their staff specializations are and whether they have a strong showing for ancient history.
There are several, but you will really want to figure out what you want to focus on on and work from there since all schools are going to have their own specialties. Also, what coursework can you start taking now that will help you with what you want to do? Even if your history department doesn't have a lot of classes in what you want to focus on there may be classes in other departments that will be helpful such as classes on archaeology in the Anthropology department, classes in area studies departments that may be helpful to what you want to do, or language classes that you'll want to have for grad school
As others have suggested, you'll want to narrow your interestes to something more specific than ancient history: Rome? Greece? Egypt? Persia?
In an MA program, you'll take classes and pursue an independent thesis project under the supervision of your advisor. So you want to choose a program that ideally has several faculty working on topics similar to your interests. This will enable you to take multiple courses on topics that interest you, and (most importantly) have an advisor to work with who will be able to guide you researching a topic that you find interesting (ie, you might not find anyone willing to supervise a thesis on Old Kingdom Egypt in a department that only has Roman historians). So figure out what you want more specifically, and then you can start finding programs that have strengths in that particular area of focus.
More generally, if you're interested in Greek or Roman history, you might want to consider classics departments as well as history, as a lot of ancient historians end up teaching classics in American departments.
And regardless of your interests (and my apologies if you already know this), you'll need to have a firm background in ancient and modern langauges to be a competitive applicant and get a good funding offer. Latin and/or Greek (depending on your interests), and French and/or German (both if you can), are pretty much non-negotiable. You can (and will) improve your language skills in grad school, but you'll be at a severe disadvantage if you have to start from scratch.
And NYU has a strong ancient studies department, which may or may not suit your interests: http://isaw.nyu.edu
What particular time/place are you looking at? With most places I know, you'll want to have the same research interests as at least one of the profs.
So, my response to all of you is essentially the same. Thanks so much for your advice.
I'm thinking that I'd really love to study the Middle East, particularly Persia, ancient Egypt, Mesopotamia... Stuff like that. Now, my school, as I've said is limited to modern western history, however I do believe it has a small Arabic program. So would it be beneficial for me to start taking classes in Arabic so that once I graduate from here, I can begin graduate school elsewhere studying the ancient Middle East?
I sincerely appreciate all the responses. My apologies for not being able to give a well thought out response at the moment, my life at the moment has gotten a tad hectic. Promise to return as soon as I can to continue discussion. Thanks again!