Tokyo is an expensive place to visit, but can be affordable for military families, US Civilians on PCS orders, and US Government Contractors looking for reasonably priced lodging. There are two government properties worth staying at depending on your budget, location, and amenities you are looking for.
The New Sanno
Room rates are dependent on your grade so its pretty cheap to stay here compared to Japanese hotels. The rooms are pretty nice, and the dining, shopping and swimming pool make for a nice getaway to Tokyo. It is often difficult to get rooms on the weekend, but if you go onto their website you can see the room availability.
The New Sanno is easy to get to via train and car, plus they offer free parking. This location is great for getting to Shinjuku or Shibuya.
If you want somewhere cheap to stay in Roppongi, Hardy Barracks is a good option especially if The New Sanno is booked. The rooms are $35/night (or they were last year) and nothing fancy, but they do offer a continental breakfast. This location is great for touring Tokyo Tower or Imperial Palace.