At the 14-17mph avg pace of most casual riders, it isn't the bike that makes you go fast, it is your legs, lungs and heart.
I have a 1983 Nishiki Olympic chrome-moly frame and Sun Tour components I bought in high school, a 2009 Fuji Paris-Roubaix aluminum frame carbon fork and Shimano 105/Ultegra components, and a 1992 Trek 1400 aluminum with period Shimano 105 and old school downtube shifters in pristine condition that I paid $400 for on Craigslist last year. The Nishiki is a 26lb steel beast and it rides like a Cadillac, and it only slows down on big climbs. I paid $400 for it brand new. It was made in Japan.
The Fuji was recommended in a bike magazine as a good buy in the $1200-1500 price range comparison against a Schwinn and something else I can't remember. I got it at the start of the recession for about $1000 during the inventory clearing end of year fire sales. If the Fuji could time travel, Greg Lemond would have easily won one or two more TDFs between 85 and 91. It weighs about 21 lbs in a 61cm frame size. It is twitchy, seems to always need a tweak of the drive train, or some adjustment. The drive train seems to want to jump gears or miss a shift and pop the chain at the worst times. It was made in Taiwan.
The Trek frame was made in the USA. At 63cm it weighs about 22lbs, and it will go a year without needing anything but air in the tires and chain lube. The drive train is smooth and feels bulletproof. I put over half of my 2,500 miles last year on this bike.
Find someone who knows old bikes and look for the Trek 1000, 1100, 1200, 1220, 1400, or 1420 series bikes from 1990-1996. The 1400s have all aluminum frames and slightly better components. The others have slightly lesser quality aluminum frames and chrome -moly steel forks. But they don't weigh more than 23lbs. Put on a modern saddle and get them tuned up and they will go forever. In pristine condition they are in the $400 range, in normal wear and tear with scratches and torn seats and jacked up handle bar tape, they are $250 ish. The older Cannondales in the same years with that time period Shimano 105 drive trains and down tube shifters are also USA made frames and similar quality bikes.
20 year old Trek mountain bikes which would be hybrids in today's world make good all around bikes, if you can find one in good shape. I have a 1989 Trek 830 steel frame Antelope that I bought new at Nav School. About 15 years ago, I put street slicks on it, and I can average 15mph on flat pavement for about 20 miles. There was an aluminum version of these bikes, the Trek 7000 and 8000 series. I paid $225 for a 1992 or so 7000 for my wife two years ago, put slicks on it and it is her road bike. It weighs about 23lbs in a 19 inch frame. The steel frame 830/850 Antelopes or Mountain Track between 1990-1996 are $200-$250 depending on condition, and weigh 26lbs in a 22 inch frame. The 930/950s are a little more robust frames and are harder to find. The 800 series were made in Taiwan, the 900s were US made and so were the 7000/8000s I wish I had not been such a poor lieutenant or I would have bought one in Sacramento. Any of these are ideal for light trail use, watch out if the 7000/8000s were ridden hard off road, those frames were early ventures into aluminum and are prone to cracks. But if you find one that was barely ridden in pristine condition, jump on it.
Vintage Trek Bikes- Information on Steel Road Bicycles made by the Trek Bicycle Corporation, bike
Good luck on your quest to find a ride. Be patient. Check pawn shops and Goodwill. Sometimes they get good stuff and have no clue what its true worth is.