If you're looking for a hotel on a budget in Tokyo, Hotel Tavinos Asakusa really fits the bill. A lot cheaper than Shinjuku / Shibuya hotels and with the fantastic Tokyo subway system, we didn't have a problem getting around at all. The location has lots of convenience stores around it if you need any food, drink or other amenities (many 24/7) and the rooms were very clean and comfortable. The hotel laundrette is also super easy to use, and convenient if you need to do a quick clothes wash.
The only minor comment I would make is that the rooms are pretty small, and storage space is a couple of coat hangers on the wall, and a small space under the bed. We both had backpacks so it was fine, but if you've got a big travel case you may really struggle for space.
Checking in and out was really easy, staff were very English friendly and had zero problems. Would definitely stop here again in Tokyo.