Looking for a room or studio in Manhattan/Brooklyn

Hi! I'll be starting a new job in Manhattan next month and I'm looking for a pet-friendly studio or room in Manhattan/Brooklyn to rent. I'm pretty laid-back, so I'd want to live with roommate/s who are similar.

A little bit about me: I'm 26, work in media, and I have two cats. Both are housetrained and good with people. My interests include reading, writing, hiking, and ecology, but I also like having friends over on occasion and going to events in the city. I love how much there is to do in Manhattan and parts of Brooklyn, so I'm hoping to find somewhere centrally located (close to subway stations, lots of stuff to do in the area, etc.) like

As far as living spaces go, I'm pretty flexible, though I definitely want an in-unit washer/dryer combo. I would prefer somewhere partially or fully furnished but it's not a requirement. A balcony/patio or terrace would be great, but that's also not necessary. My max budget is around $2000/month but I'd prefer to spend less.