Rob, I'm not aware of any explicitly boxing gyms in Astoria -- which surely doesn't mean they aren't there! A lot of times, boxing gyms in the 718s are neighborhood deals, or tied-in with the Police Athletic League. Most of the little gyms I see in the neighborhood are focused on martial arts courses and don't mention boxing in their ads/displays.
You should ask yourself how far you want to go with it, because some of the NYSC boxing instructors are pretty good and will give you a solid training in the basics, albeit without contact. Usually every fall they sponsor a "boxing camp" which costs extra, but goes the extra yard in terms of giving people solid instructions on how to box. I took one of those inititally, then started getting into regular classes afterwards. I've been training with Jose "Kid" Avila for years now and always get an incredible workout with him -- I could let you know his schedule, if interested, although I know he doesn't come out to Astoria. I'd say the main problem with most NYSC boxing instructors is that they focus on military-style calesthenics to break people down physically, but don't offer enough basic boxing instruction.
If you want to get really serious about boxing, I'd go with Kingsway or Church Street in Manhattan, or Gleasons in Brooklyn -- all of which train professional fighters and offer sparring opportunities if you're so inclined. Personally, I did some research on concussions (i.e., getting even one is not good ... can't imagine what it's like to be Wayne Chrebet and have eight ...) after getting my bell rung very badly once and pretty much decided the only way I was going to keep on sparring was if I got paid to do so. It just aint worth it to take serious head shots from someone who knows how to throw a punch unless you're good enough to win titles of some sort.
A lot of your enjoyment/reason to keep boxing will depend on your instructor/trainer, and good ones are hard to find. From what I've seen over the years, it's also simply a matter of dedication and showing up a few times a week -- I've seen hundreds of people come and go from Kid's classes over the years, some hanging in there for weeks or months, others walking out 15 minutes into their initial class. But only a handful keep doing it (and most of them women). Guys make the mistake of thinking it's a macho/power sport, but for the most part, it's speed, coordination and endurance. And it's a sport well worth learning, as it provides a usable skill.