I'm trying to make this blueprint look like a true blueprint for framing. (Blue background, white lines). But as you can see from the image, there are dark parts of the image. How do I make it look like a real blueprint? (see 2nd photo attached.)

You won't be able to turn that hand-drawn blueprint into a cad/vector like the example.
For a very rough conversion, you could try the centerline tracing in Inkscape,
but my personal opinion is that it's not worth the hassle, because it would require a lot of nod editing, straightening the traced lines etc.
I would remake the whole thing from scratch using Inkscape or some other vector.
Just because I'm not used to CAD editors.

Thanks for the reply, Nidhogg. Really I'm just trying to get it uniform blue in color. It doesn't have to be as crisp as the example. Isn't there any technique in GIMP I can use?

Something like this?

Yeah, that's about the best what you can expect with the common techniques in Gimp.

Yes! How did you do this, Ofnuts?

I'd start with selective gaussian blur, to remove the background grain.



Then Colors/Curves....

One way:

1) Since you are going to recolor, you can start with grey scale to avoid problems due to color shifts. The best way to grey-scale here is to pick one of the R/G/B channels. This is done by just dragging the channel preview in the Channels list and dragging it to the canvas. One channel may have more contrast than the others.
2) Selective Gaussian blur to even out the noise
3) Using Curves make the whole background white. The histogram has large peak, anything to the right of that peak should be white. At the other end, you can eyeball the blackpoint (the value under which everything should be black).
4) Using the brush with white, clean out the borders and all the spots in the large empty areas. Get as close to the drawn parts as you dre, but you don't need to be too close.
5) Set the foreground color to white, and the background to the blue that you want, and set the gradient to "FG to BG (RGB)".
6) Colors>Map>Gradient map