I only know of two cameras that have image stabilization and costs less than $250:
Canon A570IS and Sony W80
But image stabilization does nothing for noise.
Noise is caused by using a high ISO setting.
Of all the small cameras the Fujifilm F20, F31fd and F40fd have the best performance in low light situations. But they do not have image stabilization.
I recently bought a Canon PowerShot SD1000 and I'm very disappointed with the quality of the pictures taken indoors. Since it doesn't have an image stabilizer, the pictures are often blurry and with a lot of noise. I bought the camera after reading many great reviews about it but my former camera (Kodak CX7530) takes better, crisper pictures. Does anyone can recommend a good camera price range $150-250? I'd love to take pictures indoors and not to be too blurry. Any suggestions? any thoughts on Sony, Olympus or Kodak cameras? Thank you!