To take great blur-free indoor shots of museum and church interiors etc (without a flash) we all know you need to set the camera on a tripod, monopod or keep it absolutely still...and small digital cameras have a lot of limitations, especially in low light (because they do not perform well using ISO above 200 or so).
A digital slr is the best camera to use because of it's high ISO capabilities, however, cost and even size could be a limiting factor.
But you can do a good job with almost any digicam as long as you don't move the camera, use a slow shutter & use a low ISO for noise free pics (always use a delayed shutter release).
For Low Light performance...THE best digicam available right now that performs very well while handheld & in low light at ISO 800, even ISO 1600...is the "Fujifilm Finepix F30". It can go up to ISO 3200, however quality starts dropping higher than ISO 800.
It has 6MP, 3X optical, manual controls, amazing battery life (up to 580 shots) and a large 230,000 pixel, 2.5 inch LCD screen.
It might be your best bet, especially for high ISO but low noise, handheld interior shots....unless you don't mind trying to find someplace to prop your camera up, or lug a tripod around (not practical most times). The F30 performs extremely well in low light but does have some CA issues in high contrast outdoor shots (which is fixable with Photoshop or Paintshop Pro etc).
And don't forget that in some interiors in Europe, cameras are totally banned...thats when you have to buy the obligatory postcard...lol
Also, take plenty of photos (which means plenty of storage, I recommend at least 4-5GB or a portable HD storage device).
Have fun!