If you're looking for a base that works well for exploring both Manhattan and Brooklyn, this place should be on your shortlist.
We're a family of 5 (including 3 teenagers), and we can highly recommend Erin's place. It's a flexible basement flat/apartment, which can accommodate anywhere between 2 and 5 individuals. It has a double bed and a heavy-duty inflatable mattress in the bedroom, which ideally sleeps one adult. Plus the sofa in the living room converts into a fairly comfortable double.
Kitchen has everything you might need; bathroom is small but functional (bath + shower combo -- shower is good!) Laundry room has massive US washing machine and dryer. There's plenty of storage space for clothing.
When we arrived, I thought the place seemed larger than it looked in the photos... (which is good!)
We stayed here for a week around New Year, so didn't use the garden much. It's small, but has plenty of chairs: I can imagine it being really nice in summer...
Erin's place is around 40 mins by taxi from JFK (not too bad: Yellow Taxi from JFK = $55 incl tip; Uber XL on way back = $69).
Local transport links are *really* good. The property is three blocks to 7th Av (B, Q) and the same to Bergen St (2, 3, 4). This makes Manhattan very accessible indeed (20 mins to Canal St, 40 mins to MOMA/Met etc).
Neighbourhood is nice: brownstones on the edge of Park Slope, close to Prospect Park, dotted with coffee shops, decent diners and other options (like Berg'n).
What I'd like to recommend most of all is Erin herself. A super-helpful host, who really took care of us. She was extremely responsive on email, ready to jump in and iron out any problems immediately. Nothing was too much trouble. We really appreciated her help during our stay. (Thanks Erin!)