Will it just be you, or are you with a partner or an entire family group? (US hotels are often charged 'per room', rather than 'per person', so it can make a big difference).
However I'm finding no difficulty in finding hotels far cheaper than the figures you've suggested. e.g. the following are all fairly central:
Minna Hotel (about £48pn, inc breakfast)
Balmoral Hotel (about £53pn)
Winsor Hotel (about about £59pn)
Cable Car Hotel (about £64pn)
Oak Hotel (about £78pn)
Try Booking.com:
https://www.booking.com
Also check out Hostelworld (which has some great budget hotels, and not just hostels):
https://www.hostelworld.com
(That's my favourite website for budget accommodation. Three or four years ago I found a superb little hotel in Madrid on that site, bang in the centre of the city burt on a quiet side street, which was wonderfully clean and with free wi-fi, TV, etc for just €22 per night)