Issues of where to find a bike have been answered pretty thoroughly here, including the standard disclaimers of making sure a bike isn't stolen before purchasing.
On advice for how to see how ride-worthy a bike is:
Definitely take a look at the bike before buying. Give it a quick once-over for general wear or use. If the bike looks like it hasn't been maintained well, it will probably show. This doesn't mean it isn't a good bike, but you want the best you can get.
If you don't see any obvious signs of mis-use, check each system more thoroughly.
Keep in mind that this is not an exhaustive list, and that you will find problems with any bike if you look closely enough. It doesn't automatically mean you should look for a different bike either. What's important is whether the problems you find are evidence of deeper issues, or if they will cause problems in the future. Many issues can be fixed at home with a little effort, but it's still better to be aware of anything before you buy a bike. These small fixes can also add up if you're looking for something cheap. I'll try to point out bigger problems that you want to avoid.
History: Simply ask if there have been any problems with the bike. Has it been in an accident? was it rebuild? does it pull the left? How long has the seller owned it, how much have they used it, etc.
General: Does anything squeak or make unusual sounds? Can you stand comfortably over the frame with your feet flat on the ground? Does the bike still have reflectors in the front and back, the wheels, and pedals? Has the bike been registered previously, and can the owner produce the paperwork to transfer the registration? Do the parts have a well-greased and smooth feel to them?
Wheels: Look for wear on the tire tread. Is there any damage to the side walls of either tire? What kind of conditions are the inner tubes in? As how many flat repairs each wheel has had, and if either tire leaks air significantly.
Make sure the wheels attach firmly to the frame, and that the wheels remain secure when you torque them relative to the axle. (You don't want any 'play' in the wheels, as this may be a sign of one of those deeper problems with a loose cassette or worn ball bearings.) How are the spokes? Do they have relatively even tension on them and look like they're in good shape?
Spin the wheel on the bike, and look down the thread for any wobbling or mis-alignment. If they do, the wheels could probably use a re-alignment.
Brakes: Check the brake pads for wear. Will then need to be replaced soon? Are they aligned for proper contact with the braking surface? Do they engage quickly when the brakes are applied?
Cables: Check for any frayed ends or rusted sections. Are the cable guides still in place and preventing unnecessary wear across surfaces? Do the cables have end-caps on them to prevent future fraying?
Pedals: Do the pedals appear to have struck the ground before or they otherwise in good shape. Torque the pedal arms against the axle to see if there is any looseness. Spin the pedals by hand to ensure they rotate smoothly, but aren't too loose or tight. Also spin the pedal crankshaft to look for the same types of things. As with the wheels, being overly tight or loose at the axle may be signs of bigger problems.
Gears and Chain: Visually inspect the gears for any wear (each tooth should be symmetrically shaped, not wave-shaped). Is each gear parallel to each other on the cassette? How does the chain look? Has it been well maintained and lubricated. This is probably the only part where you would need any equipment to check your bike, but a chain-wear tool would be useful to check for a stretched chain. If you don't have such a tool handy, the aforementioned wave-shaped gear teeth are evidence of a stretched chain in need of replacement. Wave-shaped gear teeth mean the gears should be replaced also (not usually a good sign). Does the gear switching mechanism allow you to reach the highest and lowest gear, and does it move well?
Handlebars: How are the handlebars positioned relative to the seat. Are they within comfortable reach? Can you reach the brakes quickly. Are the handlebars in line with the wheel? Is the tape worn and cracked, or does it look like you will still get some mileage out of it. Do the handlebars turn smoothly in the frame with the wheel, or is there any tightness or looseness?
Seat and Post: How does the seat feel? can it be adjusted to a comfortable height and does it stay in place well. Quick-release adjustments can be a huge plus here.
Frame: How does the frame look. Is it still in line with itself or has it been torqued or bent. Are there any signs of cracks or dents? Problems with the frame tend to increase in severity with use and affect biking efficiency as the frame degrades. Some light damage might be okay here, but be aware that a damaged frame can quickly become unusable.
Ride the bike: Ride the bike for a short distance, switch through the full range of gears. Pedal hard, brake hard with both brakes (but don't let yourself fly over the handlebars), and turn a few times. How does the bike feel? This includes how the bike actually performs, and how well it feels for you specifically. Is the bike comfortable for you. If not, can it be adjusted so that it is?
Take someone with you when looking a the bike. You never know who you might come across through Craigslist, and two sets of eyes may notice more than just one.
Best of luck