Staying at Anja's place was a pleasant surprise. We stayed there for two weeks. At first, the surroundings seemed slightly confronting (litter all around) but you soon realize that that is part of NYC. The surprise was that all the hippest bars, clubs, great places to eat (Katz's Deli is a few blocks away), etc. were all just around Anja's place in the Lower East Side. On weekends, the surroundings are party central and yet Anja's place is in a nice quiet street. You can eat, drink or party all night then walk home.
Transport wise it is conveniently located as well. You can walk to different stations with different lines depending on where you're going (some are a bit of a hike, but again that is NYC, you will walk a lot). It is super close to Bowery station, the JZ line, which goes to Sutphin Blvd - Archer Av - JFK station which has connections to the Airtrain to JFK airport. The train ride takes a bit of time (and the trains look terrible - which is not unlike other NYC subway trains) but costs about USD9 to get to the airport (incl Airtrain) versus USD50+ for a taxi.
There was no TV in the apartment but we didn't miss it at all. We were out till late every day.
In summary, if you are interested in a clean, quiet place that is conveniently located, I highly recommend Anja's place.