Last summer I had the good fortune of visiting the area and I ran into the same problem. I couldn't fina anything I liked in Monaco, so I went with plan B, which was to stay in Nice and commute in to Monaco when needed. The train ride was about 15-20min and the cost was not too bad. I ended up staying at Chez Patrick
and I liked the place very much (for my review of the hostel go here
). I guess that would be my advice if you don't mind the travel time, especially that this hostel is really close to the train station and Monaco really isn't that big and walking is a requirement for sightseeing either way.
Hope that helps.