Where you're coached has a great deal to do with how much you already know. Getting time with a good coach in a good gym has something to do with the skill level you have when you show up. If you don't know much and therefore have a lower ability, those upper-tier coaches are going to spend time with students who have more promise. If you're just looking to learn the ropes, go to group boxing classes at any gym you find. It's a bit outside D.C., but Elite SFN in Ellicott City, Maryland, runs a clean and exceptional gym for beginners through active amateur ranks.
Separately, dedicating 4 months to boxing as a precursor to training for MMA is like learning tennis as a means to learn volleyball. Boxing starts with footwork, as I'm sure MMA does. They're different. The defensive considerations are different, too--and as a result of the first two, the striking is different.
If you want to MMA, start with a more MMA friendly martial art like muy thai.
Edit: one final thought. Ridgemont Raceways, which is just outside D.C., is a venue for a lot of regional amateur boxing events. Check out their promotional information, and you'll get quite a bit of insight into which gyms are sending fighters to such events. I'd start there.
