^^^Agreed. If it's near, have a look. You may not have the knowledge to thoroughly inspect the bike, but you'll be able to see if it's been thoroughly neglected or given some care.
If you're relying on the local bike shop for service, you can expect to pay full retail for parts in addition to service. So while some of the members here can pick up an 8sp chain for <$15 online and install it, you might pay $20+ for the same chain and another $10 labor. Just an example.
Regarding the chain, if it has a considerable amount of rust, I'd just have it replaced. A broken chain is a great way to lose control of your bike and crash. Even if you don't fall, you may still find yourself an unpleasant walk from home. But...
There are numerous bearings on bike, and a rusty drivetrain may just be the visible signs of corrosion on a bike left exposed to the weather. Headset, bottom bracket and wheel hubs are all bearing locations that may require service (which could be $100 labor + parts). Cables and cable housings are consumables, and the latter is especially prone to corrosion. Brake pads harden and become less effective. I don't live in a locale with snowy-icy winters, so I don't know how tires are affected by exposure in such. Some cracks in the tread alone don't necessarily mean replacement; the tire's fabric casing beneath the molded tread provides integrity; the tread protects the casing and provides the rider with traction. Sidewall damage is another story.
I'm being vebose. The "amazingly low price" may be a sign that the bike really does need genuine attention. If it's a more of a project bike, I'd let it be a deal for the home mechanic. It could require a complete overhaul (~$150 labor) plus parts.