Doomed,
I was based at Atsugi for 3 years, it's a great place, I really enjoyed it. If you get free time during the week while you're there, Hayama/Zushi/Big Budda (Dai Batsu?) are easily reached by train. Since you're out that way, you might also try to swing a trip out towards Hakone National Park, close to Fuji.
If you're staying at the BOQ on base they have nifty xeroxed maps with directions to all the close-by attractions. Even for an evening out you can catch the train into Tokyo, it takes about 1+1/4 hours total trip either from Ebina to Shinjuku or by connecting through Yokohama to Shinagawa. By the way, I hope when you arrive that you are taking the Narita Express train straight through to Yokohama, then connect to the Sotetsu line for Sagamino. This is much nicer than the van/bus they run between base and the airport. (though connecting at Yokohama station is pretty crazy!) Here is a link to a Sotetsu Line page if you're interested
Sotetsu Line
I don't know if it's possible, but you could try to arrange lodging in Tokyo at the New Sanno Hotel. It's a DOD facility, a real hotel, however rooms can be tough to get at short notice on weekends. And you must have a certain status. Not sure of the rate these days, but it used to be below $50/night a few years ago.
I would not go all the way from Atsugi to spend a Friday night at Disneyland. That is a very long trip to make just for an evening there. Plus, you then have a hotel to deal with. Difficult logistics there. I think a night in Roppongi is time much better spent, kind of a Disneyland for adult gaijin!
Have a great time there! If there's anything else you want to know about the immediate base area, restaurants, etc. just let me know. (make sure you have lunch at the awesome little soba shack on base!)