We really enjoyed our stay at Shelley's garden flat. The bed was comfy, the shower pressure was great and the place was spotless. We arrived late but Shelley had popped the keys in a lockbox and given us the code ahead of our flight, so it was really easy to access.
The apartment is less than a 5-minute walk from Newkirk Av on the 2 and 5 line, or from Cortelyou Road on Q and B. It's then about 15-20 mins to Atlantic Av in Brooklyn or about 45 mins to central Manhattan.
We didn't really get a chance to spend much time in the immediate area as it was our first time in NYC and we spent most of our time in Manhattan. But Shelley has some great knowledge of Brooklyn and is great for helping with recommendations!
Get a taxi from the airport as it takes less than 30 minutes (off peak) and only costs about $8 more than the train, which takes over an hour at best! We didn't follow this advice when we arrived and massively regretted it!