I stayed at Night & Day a few years ago. It was really close to the Trevi fountain, I walked past it several times every day. I paid 70 euro a night. Decent place. Your own bathroom. Shared kitchen. Close to everything. And the lady that ran it was super nice and helpful. Pointed out the best gelato and places to eat. And I would have missed my train if she hadn't informed me of a train strike.
www.nightanddayplace.com