Hey all,
Thought I'd stop by to give an update for future reference as I imagine this topic will come up more and more.
Due to my NH flight arriving early, I was able to buy my Monorail ticket by 5:05am and waited for a rapid service to Hamamatsucho. As mentioned before, I hadn't been to Japan in over twenty years but found the process of buying the ticket, taking the monorail, transferring to the Oedo Line at Daimon and ultimately getting to Tsukijishijo station. Unfortunately for me, the market was closed today but I wandered nearby and eventually had a nice sushi breakfast for about 3300 Yen. I started to head back around 7am, and definitely noticed that both the Monorail and Daimon station were much busier than when I was first heading into town.
As for immigration and customs, I wasn't sure what to put down for my purpose of visit and also left the address blank. After explaining to the man at immigration that I just wanted to leave the airport for a few hours, he told me to write down "Haneda transfer". Customs stopped me and I had to explain once more that I had a flight later in the day but wanted to leave for a bit. In addition, customs also inquired as to the whereabouts of my luggage.
In addition, I was surprised by the length of the lines at security when I was leaving. They moved at a reasonable pace but I wasn't sure why they couldn't open a few more lanes. Just leave some time to get through security as I didn't notice any lanes for elite flyers.
Thanks for all who supplied advice and suggestions. I had a great time and definitely want to visit Tokyo for a longer period in the future. For those who are unsure about leaving Haneda, my advice is to go ahead and do it.