You have plenty of time to grab a nice meal. Assuming you land on time and setting aside a generous 2 hours for customs + transportation from Narita into Tokyo (Keisei train line or Narita Express train), you'd arrive at 2000, which is plenty enough time for a pleasant late dinner, some city exploration, and then crashing at the hotel for 8 hours of sleep. From the city center (Shinjuku, Ginza, Tokyo Station, wherever) it's about half an hour to get to Haneda on a train.
There are English signs everywhere when it comes to public transportation, and most station attendants can speak enough English to give you directions. I'm biased because I've been to Japan a few times already, but I assure you the city is not difficult to navigate. Google Maps works just fine.