Ibiza recently closed. Also, ctforbes mentioned Poets & Busboys. It's actually Busboys & Poets.
I rarely go out. There are a number of restaurants and bars along 14th St NW, particularly north of N and south of V St/Florida Ave. This intersects U which is also pretty busy between 7 and 16 Sts. (Howard U is just a few blocks north of U & 7th/Georgia Ave.) These spots usually have a lot of traffic and can be good for people watching. The "gayborhood" has sort of centered around this area and surrounding streets. It's not explicitly gay or anything and the area is popular with millenials and locals, in general, because of the close proximity of things (bars, food, Trader Joe's and Whole Foods, Target and a few other shops a few blocks north at Columbia Heights), but some businesses sport pride flags, and there's gay sports bar Nellie's at 9th St and big gay club Town at 8th. As gentrification has spread, restaurants and bars have appeared on some adjoining streets too.
African King mentioned Gallery Place. The Gallery Place/Chinatown shopping center is somewhat limited. There's Urban Outfitters, Bed Bath & Beyond, a sports store and a few restaurants, but most of the interior is taken up by a movie theater and a bowling alley/bar. There are a few places scattered around the area west of there. There are a few recent additions a few blocks NW from there at CityCenterDC, a fairly new mixed-use development. It has some fairly high-end retail and a few new restaurants. Some foodies were hyped for these new spots Momofuku and Milk Bar. I believe the other American locations are all in NYC. Georgetown might be okay for a stroll, though it might be more of a tourist destination.
There's a strip of bars in Adams Morgan, 18th St NW beginning around 18th St NW and stretching a few blocks north. There's a few sorta wacky themed bars along H St NE but I'm not sure that many treat that area as a destination, more like something for those in the neighborhood. About a mile and a half south, there's a restaurant in the Eastern Market area named Rose's Luxury that's gotten really good reviews. I hear there are two gay bars popular with black guys. I think they're dives and I'm not sure what kind of crowd they attract: The Fireplace and The Bachelor's Mill. Generally, I hear people say their experiences there are interesting rather than particularly good.
So yeah, U St is probably the loudest place during the weekend. I've heard of a monthly spanking party at a certain bar that will be occurring during your visit, but I don't think that's what you have in mind.