These are 3 of my recommendations. I never actually paid to stay there but I have sneaked in when my friends from overseas visited me.
Recommended if you prioritize: onsen and access to Harajuku
The lowest room rate for 2 ranges: 194 - 250 USD
The hotel is located just between Harajuku are and Shibuya, so if you are into shopping, this hotel is perfect. One of the highlight of this hotel is onsen where you can relax after long shopping day!
Their room is quite spacious and well-cleaned. You will be comfortable at this hotel.
Recommended if you prioritize: access to the station and cool room design
The lowest rate for 2 ranges: 122 - 160 USD
Granbell Hotel is in 3minute-walk from West Exit of Shibuya Station which is easy to get on JR Yamanote line, Toyoko line, and Fukutoshin line. If you are planning to not staying in Shibuya but explore various parts of Tokyo, this hotel would be a convenient hub.
Most of the room is well-designed, but some has interesting theme like Bear Room.
Recommended if you prioritize: direct access to Shibuya station and airport limo access
The lowest room rate for 2 ranges: 192 - 300 USD
Excel Hotel is directly connected Shibuya Station so I can almost say this is the hotel that has THE BEST ACCESS to station! Great clean room with a good service. The hotel is one of the pick-up/drop-off location of Airport Limousine bus to Narita and Haneda. It is pricy but if you don't mind paying for the convenience, this is a great option.
It is also directly connected to Mark-City which has many restaurants and shops.