Unfortunately, I can't read Bakari's link (firewall at work blocks all of blogspot), so if this repeats everything he says, sorry. If it is totally against what he says, well, then at least your getting different opinions right?
Things you can do to keep the bike on the road and make it better:
-Put narrower tires on it. A lot of those old Hybrid used big huge balloon tires for comfort. If the wheels are 26", look for something like a 26x1.25" tire. If the wheels are 700c, go with a 700x32 or 700x35. If the wheels are 27" give a lot more consideration to replacing the bike (27" tires are largely discontinued. Your choice for new tires is very limited, and will only get worse). The narrower tires will reduce drag (making the bike faster) and reduce the effects of head winds (a very little bit).
If you take it a shop they
can replace the handle bars with drop bars (what most road bikes have). The fact it can be done does not always mean it should be done. It will change how the bike fits, and it may make the bike less comfortable.
Those three speed internal gears are great if you ride in the wet all the time, but they definitely limit your ability to ride into the wind or up hills (when you just want to keep droping down gears). You cannot replace it with an external gear system, but you could replace it with a modern interal gear hub with 7 gears. I do not recommend this, as those things cost a fortune and you'd be better off buying a whole new bike.
You can have the frame sand blasted (inside & out) to remove all current rust, and then have it sealed. Unless this bike is a resotration project of love, it really isn't worth the money.
You can ask all the local used bike shops if they have a similar frame you can swap out. It'll be cheaper than buying a full bike.
So, while those are all options, I'm not really sold on them being great options. Bike technology made some good strides in the 15 years after your bike was made, and I'd be much more interested in looking into a steel* road bike (with 700c tires) from the mid 80s. Most the names you listed are good bikes. Bianchi in particular always made really good bikes. Raleigh and Schwinn I'm less fo a fan of (though there were much better than they are now). Peugot is supposed to be good, but I've never ridden one.
*From your perspective there are actually two types of steel, High tensile (often just called Hi-Ten) and The Good Stuff. The Good Stuff can be cromoly, it can be 4000 series, it can be easton or reynolds tubing. Really, it is anything they use to make steel frames that is not Hi Ten. Hi Ten is cheap, heavy, rusts easily, and really isn't a material of choice. I'm going to also suggest avoiding Aluminum frames. They don't rust in the same way, but they transfer a lot of shock (bumps and pot holes). Unless your city has pristine roads, I'd take a steel frame given the choice.
If you can find a bike that was intended as a touring bike (Trek 520, Rocky Mountain Sherpa) you'll be set. These bikes are very strong and reliable, comfortable, and can carry a lot of stuff on proper racks.
Depending on your budget, and how long you plan on keeping the bike, you should consider buying new as well. But not a 2012. Check with your local bike shops and see what inventory they have from 2011 or better 2010. Any 2010 left overs should be seeing a huge discount. If you ask nicely, they can also check their suppliers warehouses to see what old stock the suppliers still have on huge discount.
For example, my current commuter is an aluminum flat bar road bike (also called a performance hybrid). Its a nice bike, but the roads are just too rough for it, so I've been looking for a steel framed light duty touring bike. None have come up used in the last 9 months I've been watching. So, I started calling around the bike shops. I can get a lasts years Brodie Romulus
http://brodiebikes.com/2011/bikes/romulus.php for $580, instead of the $900 new. I also found hiding in the back of another shop a 2010 Norco Fraser
http://www.norco.com/archives/2010/?id=fraser for 50% off of the $985 MSRP. I bought that one. After tax it was only slightly more than $500, it'll last me forever, and if I ever decide to bike across Canada, it'll do it in comfort.
Back to your original question: Fix or replace? I'd say a lot of it comes down to love. Do you like the bike. Does it do what you want and do you enjoy riding it? If so, keep it. Trying putting narrower tires on it, and do something about the rust. If the bike isn't that great, start keeping an eye out for a replacement. Go to a bunch of bike shops when the weather is nice and trying riding a bunch of different styles. If the upright hybrid isn't for you, try a flat bar road bike and a drop-bar road bike. Look for an 80s steel bike, and ask all the local shops about old inventory.
A bike you love is a bike that will get ridden often. If riding it is a joy, you'll make excuses to ride it. If you don't love it, if riding it is a chore, it doesn't matter how little you spent on it. You can have a bike you love and be frugal. Just make sure you remember that sometimes being frugal means paying a bit more up front than being cheap (being cheap always costs more in the end though).
