I decided to tackle the front hub on my 80's schwinn sprint. Disassembly when fine, got everything cleaned up (bearings are in a cage not free), regreased, and put back together. The problem is there is some "play" (side to side) when the wheel is attached to the bike? Not much, but noticeable if you push on the tire. If I tighten the hubs any tighter, the wheel does not spin smoothly? Did I put something together wrong? Will the "play" damage the hub or rim over time if I ride it like this?

It's a fine line between too loose and too tight. Might take a few attempts at adjusting the cones again to get it as good as it can be. A little bit too loose is better than too tight. Maybe the cups and/or cones are worn?

In short - yes - the play will damage the hub - the more play in the hub, the quicker the bearings will wear and deteriorate and the worse it will get. If you're going to the hassle of disassembling a hub, I'd always dump the old bearings and replace them with new, virtually regardless of their state - bearings are cheap, your time is valuable

Clean up the bearing cups on the hub and the faces on the cones and look very closely at them in good light - are they nice, shiny and generally, perfect? If not, get some new cones from your LBS. Hub races are more of a problem... Finally, when you reassemble, pack the bearings in *lots* of grease. Also, clean and grease the threads on the cone and axle end you're working on - this will make final bearing tension adjustment a little easier.

If the bearings, cones or cups are less than perfect, the rotation will never be perfect - the less perfect the surfaces, the harder the adjustment and the less perfect the end result.

Would you recommend ditching the cage and fitting loose bearings?

I am not a fan of these cages, I once had one break on me and it made a mess of the cone and cups.

Oops, yeah, meant to say that as well. The cages make installation and removal easier (if you do it a lot ) but, as you say, they make a right mess when they start to corrode. Dump it and fit loose bearings.

On a bike that old I'm betting that your cones are pitted. If they are pitted even a little bit it makes you choose between loose and crunchy feeling.

People talk about going to your LBS and picking up a new pair of cones like they'll have a drawer of them. It probably won't go that way. There are a gazillion different cones so it's probably going to be a special order deal. Good luck.

If you can't find cones that are a pretty close replacement, you'll have to decide between slightly loose and a little crunchy. Ultimately replacement wheels are probably in order. After 20 years the rims are likely to be a little iffy anyway.