Red, I'm not sure what you mean. If your images are displayed at, say 256 x 256 pixels, and that is their natural resolution (i.e. the .tiff or .png or whatever has 256^2

), if you try to shrink the size at which you display them, then you MUST lose resolution (your screen can't physically resolve anything smaller, and your imaging software will average adjacent pixels to accommodate for display).
Now, if they're being displayed at 512 x 512, which is 2x their natural resolution, then you can get away with this, shrinking the image won't reduce their display resolution, because its still greater than or equal to the natural resolution.
I've heard good things about gimp (never tried it) but I've found FIJI able to do most basic operations (and many advanced) on images. Changing the natural resolution of an image is as simples as image > adjust > size and changing the display size is as simple as pushing "-" or "+." It's a good piece of freeware.