I ride a 1993 Trek 1200 with 700x23c tires. The rear hub finally died when I hit a curb hard the other day; with the severely worn rims on top of that, I'm finally in the market for a replacement set of wheels. I ride to class and for fun on this bike, so I don't need a top-of-the-line set. Are there any quality wheels under $300 out there that take 7-speed cassettes and 700x23c tires? If not, will it be cheaper to just have new wheels built rather than buy a $400 or $500 set?

Front wheel will be easy to find a cheap one - you could probably get a perfectly decent lightly used front wheel on Craigslist for something between $20-40, $50 tops.

If you need 7 speed, and you're on a budget, I would recommend getting a rear wheel that takes a freewheel, rather than using an integrated free-hub and cassette. It's very possible that that is what you already have on your bike, but I'm not sure, because the early 1990s is when most bikes were moving toward integrated hubs.

My first question for you would be, what is the spacing between your rear dropouts? It will either be 130mm or 126mm. If in fact it's 126mm, it will be very easy for you to get a standard freewheel type rear wheel. Here are a couple that sell on ebay, for well under $100:

Wheelmaster 700c Alloy Road Hybrid Rear Bike Wheel Silver QR Freewheel 126 | eBay

Sun M13 Rear Wheel 700c Silver Fits Vintage Road Bike 5 6 7 Speed Freewheel | eBay

With either of these wheels, you'll also need to buy a 7-speed freewheel. These typically sell for $20-25 each.

If in fact, the rear dropout spacing is 130mm, it complicates matters, because most wheels built for 130mm spacing nowadays are mainly compatible with 8,9, or 10 speed cassettes. Some might be able to take a 7 speed cassette with a spacer. Here is one that the seller claims will do exactly that - although I cannot speak to how good this wheel is, all of the components are reasonable:

Alex R450 700c Black Cassette Type Road Bike Rear Wheel 130mm Fits Shimano SRAM | eBay