I need to watch my budget- a trip to Tokyo is expensive enough for me. And while I would certainly not consider it cheap, I feel that the Hilton Tokyo Bay offers by far the greatest value for money around the Tokyo Disney Resort! I have stayed there for 4 nights in March 2012 and loved it. I can recommend it without hesitation, and will stay there again for sure!
The monorail station is almost in front of the hotel, it's just a 2-3 minute walk. You could also take the free shuttle bus, but for me it was faster just walking. Like BelleBway already said, you exit the Monorail at Maihama station and take the train into Tokyo from there. The express train just takes 15 minutes to Tokyo station, i think the slow train takes about 30 minutes.
The Hilton Tokyo Bay is a very nice hotel. Staff was superb! They were very friendly and all of them seemed to speak excellent English. The rooms either have a view of the two Disney theme parks (behind a large parking lot) or the beautiful Tokyo Bay, where you can see the skyline of Tokyo and even Mount Fuji on clear days.
My room had a standard yet very modern look, though I saw that they also have some "magic rooms" for families. I had a newspaper delivered every morning, and the usual amenities such as slippers, coffee maker, etc. The bed was extremely comfortable.
Breakfast was good with a western selection including the usual: Waffles, pancakes, sausages, bacon, scrambled eggs, bread, rolls, lunchmeat, cheese,....On top of that they had some Japanese items that I've tried but didn't really care much about to be completely honest, but that's just me.
Again, I can really recommend this hotel!!