The area around the Country Inn is one of former factories, different City authority buildings, small restaurant businesses, and a kind of "Hub" in Queens for transport. You will be within brief walking distance (less than 5 min.) for all of the subway trains at Queensborough Plaza (elevated at that stop), and less than a 10 min. walk for the underground subway trains at Queens Plaza (slightly East, in the opposite direction from the Queensborough bridge). The hotel concierge will help you sort it out. Actually, you can walk across the Queensborough Bridge into Manhattan (many people do it even to commute -- It's about a 30-min. brisk walk (faster if you're very fit, slower if not)--I have done so many, many times). Walking, as well as taking the buses, brings you to the juncture in Manhattan where 3rd Avenue meets 60th St. (and where the tram for Roosevelt Island stops). At QBorough Plaza you can take either the Q60 bus across the bridge (its last stop is right there across from the Roosevelt tram) or Q32 (which keeps going down 60th to 5th Ave., then turns Southward, eventually ending at Penn Station/34th St.
Good food options nearby:
If you get onto the Q or N trains and continue Queens-ward, disembark at Broadway or 30th Ave. You're now in Astoria, Queens, where the highest number of Greek people outside of Athens live. There is great Greek food everywhere, and a great mix besides (Brazilian, German, Latino, Irish, Romanian, Korean, Italian, Indian, Pakistani). Suddenly you are no longer in a post-industrial hub but an actual neighborhood. I would suggest getting off at Broadway and trying at least one restaurant, like Cafe Omonia. Their coffees are WONDERFUL, and they have so many pastries you won't know what to choose. http://www.omoniacafe.com/
You can eat in Manhattan all the time, of course, or get the best Patstitsio, Spanikopita, and especially Moussaka this side of Greece itself. (I gained a lot of weight having Moussaka from Pinocchio Palace, 32-02 30th Ave, Astoria, NY 11102, 718-721-9636...Addictive!)