Recs between BAM and Nu Hotel?
I live a block from the NU and routinely walk between the area where iCi is and my apartment. The one thing I would say is that Schermerhorn and Livingston are awfully dead at night; I'd choose to do the walking on Atlantic just to be safe. (There are a lot of construction projects and little to no pedestrian traffic; there's not a history of problems, it's just looking out for yourself and being smart.) That said, the walk between iCi and the NU should be about 25 -30 minutes, about 10 minutes longer than it would take to get to BAM. NOte that both iCi and the NU are relatively close to the G train.
As for places in between that would be recommended, you'll be close to the northern-most reaches of the Slope, so Franny's and Taro Sushi aren't too far away. Near the hotel you'll find various restaurants, from the new Bueno to the Michelin-starred Saul. As for places directly in between BAM and the NU, the best food recommendations I could make would be Bedouin Tent for Palestinian (not really a destination restaurant) or perhaps Jolie for French. Stan's is "cajun" and I've found it to be hit or miss, but others have liked it. Other than that, I can't really recommend any other dinner options.