Keep or trash?
 

The wheel below has some rust. In the second pic is the wheel with the rust removed. The chrome shines where it's intact but there are spots where it's peeled away or pitted. Coating the wheel will prevent future rust and structurally the heavy steel will be fine but is there a reason to keep the old wheels? In particular these are Schwinn S6 rims which can be pretty easily found still.

Secondly, this particular bike also had frame rust. After removing the rust, the paint underneath the rusty area naturally was gone. Again is it worth keeping as it protected, repainting, or just dump it? This is a 57 women's traveler. Would the answers be different for pre war bikes? This particular bike wasn't ridden more than a few times, the tires are still good, and it could be parted out for the hubs, badge etc.

Rusty Tire: http://i.imgur.com/jyTSaEs.jpg
Rust free with flakes/pitting: http://i.imgur.com/Bohd2YU.jpg
Up close http://i.imgur.com/2Wky4be.jpg

Fork http://i.imgur.com/tNM0Na1.jpg

Have fun, but consider it a labor of love.

That bike in pristine condition probably wouldn't break $200.
In good rideable condition, maybe $100 to $150.

A lot of vintage steel rims from the 80's or 90's might be replaced with aluminum. But, that one.. I'd probably keep with chrome steel.

Does it have spokes now? Or did you remove all the spokes?

I'd probably strive to keep costs down on the restoration, but it really is up to you, and your goals.

The spokes were rusty as well and most probably not safe with the rust removed. The process is practice but I'm leaning towards just parting it out. I need to practice on some hubs anyway. This one did come with a bag and booklet :)

Unless the bike has some sentimental value or your lady friend really wants it restored, it sounds like this is the perfect parts bike for a late 50's Schwinn resto. There are plenty of better candidates for that on our local CL right now.

I'd only keep the rims if I was desperate - or possibly building something with coaster brakes. Never know when you may need a replacement fork though.