While Cornish Game Hens, a particular variety of young chicken, is considered a fine american breed, it does not appear to get a great deal of attention from New York restaurants. A Google search reveals very few New York City restaurants that specifically serve Cornish Games Hens, or identify their chicken as such.
One place which has it one the menu is Chez Napoléon, 365 W. 50th St., between 8th and 9th. This is an old time classic French restaurant, of the kind which used to populate the theater district, with an unchanging menu of standard classics. I have not been there myself, but I understand that it is tried and true, and fairly reasonably priced.
Now, their are numerous places which do amazing roast chicken, albeit not your preferred breed. I highly recommend the roast chicken at Nomad on Broadway and 28th Street. The skin is injected with foie gras, black truffle and brioche stuffing. Nomad is very expensive, the chicken dish alone, which serves two, is eighty dollars. However, it is not something you think about during sex, it is sex, and very good sex at that
but thanks for trying to help Jack. Cornish Game hens are baby whole chickens, not just thighs and breast 
lol that has a double meaning doesn't it?LOL