You're looking for a rental and your budget is capped at $1800/month. This Curbed Comparisons has got you covered. Thanks to the folks at Zumper, you can get a look at rentals in this price range all over the city. Have a look.
↑ This studio in the California House is only 486 square feet, but it's in one of those Kalorama buildings that feels like a fancy hotel from the 1920s. At $1725/month you can get your own balcony, but you'll have to share laundry with the building's other residents. Also, the pets cannot come along.
↑ This one bedroom apartment at The Fitzgerald is pretty spacious at 871 square feet. The hardwood floors definitely stand out, but the building amenities are pretty impressive for $1725/month. A dog park, a grill and fire pit and private parking all come with the rent. You'll be sharing laundry though, and the gym hasn't quite arrived at this Mt. Pleasant complex yet.
↑ Some of the services available at The Loree Grand make it sound like you're staying at a hotel instead of renting a one bedroom apartment in NoMa. The building has coffee and tea service, fresh cookies in the afternoon, valet dry cleaning and available maid service. Not bad for $1720/month. It's also a building that will accept your pets, but they won't accept your nicotine habit.
↑ Just a few blocks south of the California House is this larger Adams Morgan one bedroom apartment. It's $1750/month to live in this 650 square foot space with a balcony and huge closets in the heart of a nightlife destination, but 1860 California Co-op is indeed, a co-op, so keep that in mind now if the mere sight of that word sends you running to the hills.
↑ Waterfront is growing and a studio by the water may not be $1700/month for long. This one is in Potomac Place Tower is pet friendly and that honeycomb window shade is pretty fun. Additionally, off-street parking is available and the building has a swimming pool and a gym.
↑ The $1750/month does not include electricity and gas at this one bedroom Logan Circle apartment, but it does get a washer and dryer that won't require coin activation or even sharing it with anyone. Pets are not welcome and at least a twelve month lease is necessary for this 555 square foot space.