Looking for a 2BR

I am looking for a 2BR (an actual 2BR not a second bedroom that is actually a tiny home office or a room for a baby) in the $2,600 and under price range (less if going through a broker).

I'd like to be in any of the following neighborhoods: Brooklyn Heights, Dumbo, Carroll Gardens, Boerum Hill, Park Slope, Ft. Greene or the western part of Prospect Heights (i.e., west of Vanderbilt). Basically any prime Brooklyn neighborhood except for Williamsburg.

Things that matter to me include:
1) Clean well kept places, e.g., vermin free.
2) Close to the subway (<10 minute walk)
3) Responsive and nice landlord
4) Equal sized or similarly sized bedrooms

I'd prefer to find something no fee and for June 30th. I will however accept a June 15th or June 1st for an awesome apartment.

If you know of any places, are vacating a 2BR or know a broker who is good and will not waste my time please let me know!

BTW is what I'm looking for realistic these days? I feel like it is!

Thanks in advance!