I would heartily second what Conficius said. As one still in the U.S. military reserves, I know from experience that you merely need to ask whilst here visiting in the States. It is not considered "forward" or cheeky but merely something that the resteraunt/fun park/retailer etc. might not have posted. Even places like New York city (that you would think is far from a military base) offer a lot in this regard.
If they pause as they consider that you are non-U.S. military, I would recommend that you simply mention what forces you are serving with. For example even the most head-in-the-sand of my American countrymen now knows of the sacrifices that the British cousins are making in Afghanistan at the moment so a lot of these merchant discounts will be afforded to you as well. I can guarantee you that no one, and I mean no one, will look sideways at you if you pose a polite query regarding a mil discount.
The list in the U.S. can be almost endless. Amtrack for train travel in the Northeast U.S, amusement parks, mobile phones etc. Give it a try. It can be no worse than when I ask if we can take the quick route to the hotel after landing in LHR!