There are a ton of entry-level $800ish road bikes.

Unfortunately, $800 is pretty much only going to get you Sora or the equivalent. There's absolutely nothing wrong with it, you can rack up thousands upon thousands of miles on that level of equipment. It's probably 10 times better and more robust than what came with your Schwinn, and that lasted you 25+ years.

I'd avoid the Bikes Direct crap unless you are an excellent mechanic. The bikes are more or less the same as any other bike, but warranty support is limited and most LBS's these days will give you at least a year of free tune-ups. You're only saving money if you don't need a mechanic.