Husband's birthday and tried several Rick's and Trip Adviser places but full- Apr. 29 to May 2nd
Rick lists a couple of room rental services in his guidebook (or at least used to). I rented one through a service listed in his 2008 guidebook. It was one floor of a building in the heart of old town (2 rooms plus bath) and inexpensive. There were nicer rooms listed at slightly higher prices, but I wanted one with a washing machine. The 2 services listed in 2008 were Futura Travel (www.futura-travel.hr) and Natale (www.rovinj.com). I think I found my room on Natale. Sent an e-mail through the website and the owner confirmed prices and availability, but you could probably also send your requirements to the service and ask them to offer suggestions.
When I was in Rovinj in July 2009, I stayed at Villa Melita, www.villamelita.com. It's about a 20 minute walk from the old town, but it offers very nice accomodations and at that time the prices were reasonable. I'm not sure what the prices are today. I do remember that the taxi fare from the bust station to Villa Melita was roughly equivalent to $12. Good luck. Happy travels!
Just an added note to say that the person working at Futura (she didn't give me her name) was very helpful. We arrived by bus and sought her assistance with finding a room. She made arrangements with an elderly lady who had an extra room (with a shared bath) that had a beautiful view overlooking the port. At night, it was a bit noisy until we figured out how to close the shutters. The price was modest and the Futura agent was trustworthy.