I'm in the middle of researching the update of Frommer's EasyGuide to New York City, so have seen most of the hotels in the Times Square area. I'd agree with PHeymont that you should extend your search beyond Times Square. Really, you only want to stay there if you're planning on seeing Broadway shows every single day of your visit. Other than that, it's the most crowded area of the city, so you'll be fighting for space on the sidewalks each day, and it has the worst food options in the city. Really, any other neighborhood is preferable, and if you're going to be here over a weekend staying in the Financial District would get you a really nice hotel rooms for well under $300 a night for the three of you (since those hotels are mostly booked by business people during the week; you'll be quite near the ferry to the Statue of Liberty & Ellis Island, the 9/11 Memorial and other terrific sightseeing down there and can hop a subway and be in Times Square in 15 minutes flat).
If you MUST stay in Times Square, don't do the Hudson (rooms much too small for the 3 of you and a good 15 minutes from Times Square). The Mayfair often has excellent rates, but its rooms can be tiny too, so make sure they'll actually accommodate your party. The Ameritania is actually quite nice and has spacious digs, though it gets a LOT of school groups in the summer months, so may already be booked. I like the Washington Jefferson, too (very nice staff though PHeymont is right, it's a bit of a walk west from Times Square), though some of its rooms will be too small for you (not all, and the pricing often doesn't follow room size there so call and ask). I really like Citizen M, though you'd have to get two rooms for the 3 of you, and that would probably bust your budget.
Another idea: the French Quarter Guest Apartments. You get cooking facilities there, which can save you money and it might be in your price range. The apartments there are also more roomy than many places, though it is two long avenue blocks west of Times Square. Another similar pick would be Hotel 414.
You'll find my complete reviews for all of these hotels on this site (just go up to the top of this page, click on "Hotels" in the black bar and then on New York City). You'll also see, in the left hand column of that page, my tips on accommodations, which includes advice on which areas to stay in; and my tips for saving money on hotel rooms.