How do I find accommodation in Manhattan?

Hi there me and my partner ( we are a same gender female couple ) are looking for a place to rent short term in Manhattan commutable to the upper east side. One of us is training for the United Nations relating to a post graduate degree the other is touring but still reciving a wage. We are looking for somewhere to stay from 17th January for exactly 89 days. We have a budget of around 1500$ per month and would like a studio preferably or would consider sharing with a gay friendly housemate. We are British one of us is from Yorkshire so I thought I would mention that as we tend to help each other out if poss and the other is half Lebanese. We only found out last minute about the training and were really worried that were either going to rent in a bad area or not going to find anywhere at all. If any friendly expats have some connections and would like to help a Northern lass out I would be extremely grateful and also if anyone in the future needs help setting up in London we would much obligue. Please no creepy guys or axe murderers. Thanks