Pioneer SX-1050: worth repairing?

In my opinion, that Beast is worth every dime of the $350 to repair....just one thought...it might also be worth the money to buy a used laptop and get the radio signal digital. Almost every station has an internet feed, and the sound will be much improved.

I think the money would be well spent for this classic piece of art and sound.

Do you trust the shop who gave you the quote, or was this a manufacturer? Long ago I had one channel go out on my Rotel Power amp. I paid a local shop $20 to diagnose the problem. They told me that all the output transistors were blown and the repair would be $220 (only paid $400 years before). I called Rotel and they actually refered me to one of their techs. He said it sounded unusual and maybe I should send it to them. They charged me $75 parts and labor, not one transistor on the repair invoice.
That shop had a bunch of used stuff out front for sale. People decided it wasn't worth the repair and just left them there. I think I know why.

I would probably get fixed because it would be hard to replace it for the price. But I would send it to someone who specializes in rebuilding vintage equipment and have it completely gone though and have any parts likely to break replaced.

A reputable shop will usually, on an older piece such as this, elect to include a complete re-cap when doing this sort of work. I had a Pioneer sx-2500 with a blown channel, and when I took it in for repair the tech said that a complete replacement of all electrolytic capacitors was advised and it would run about $300. This included a year warranty.
New caps shoould be good for ten years plus, so if you like the 1050 and can justify amortizing the expense over ten years it's really pretty cheap. Selling it with a blown channel is pretty hard to do unless someone really wants it for parts.

I also vote for fixing it. The SX-1050 was one from top of the line in what many think were the best built receiver series Pioneer ever made. I have it's big brother the SX-1250 which I fully recapped, and its a very nice receiver.

If you go to the AK board, they have a Pioneer section. The folks there can reccomend some good techs who specialize in vintage Pioneer - there'a guy called Mark the Fixer who has a very good reputation (I've never used him, but I've met him and he seems like a straight shooter).