Pankaj Purohit , May 02, 2009; 04:32 a.m.
Its good to hear that you don't shoot with flash While shooting Indoors, flash flattens everything and the 3D effect gets dead (my opinion and taste, as I do lot of architectural photography).
While shooting indoors, the tripod and cable release or a remote should be used to get sharp pictures. As you said you get a lot of noise, that is because you are using auto ISO and maximum shutter speed so the pictures get a lot of noise because your D60 uses higher ISO at the speed you set and is not as greater at higher ISO as the D700 or D3 are.
For getting minimum noise you should set your camera at ISO 200 and than use the tripod to ignore any motion blur possible because when you will use a lower ISO like 200 or 400, you won't get sufficient speed to handle your camera in your hands and hand held will definitely get some blurs. Hand held shooting needs more practice and luck in low light shooting.
I think you will normally get shutter speed between 1/15 to 1/90 in different interior low light conditions at the lowest possible ISO.
Lenses are also concerned here and I think your are using kit lenses which are also not capable to handle low lights in hands.
For exteriors there shouldn't be any problem in Auto mode. The thumb rule for bright sunny day scene is shutter speed 1/125 @ f8 with ISO 100 speed. If your camera meter says the same like this than the shot should come out okay.
It would be better to post some sample shots taken by you here to understand a bit more.
I am posting a shot taken by me :
Hand held shot taken with Nikkor 28-80mm 3.3-5.6G lens at ISO 400 kodak film (you can concern your D60 ISO 400)
(You can also have a look at my this folder: http://photo.net/photodb/folder?folder_id=900748 where all the interior and exteriors are taken without tripod because I forgotten my tripod at home and the trip was 330 km away from my home, I have recorded information about lens and iso with every shot so you can see that also :
Kodak ISO 400 film, Nikkor 28-80mm 3.3-5.6G lens, Hand Held