Gah! I just went through this over the last few weeks. It's been ages since I've had a bike and finding what I wanted was difficult. Let's go through a few things - I hope this can help others in the future in this same situation.
First things first - you'll want to avoid department store "bikes." They may have recognizable names and look cool, but they're almost all made by one company and use very low quality components. If you'll be riding once in a while with the kids or for short jaunts, then they're passable, but they're nothing to really hold on to or wont for.
Second - spend some time learning about all the components of a bike, the different bike types, basic maintenance, and rules of the road. Reddit
https://www.reddit.com/r/bicycling/ or bike forums
http://www.bikeforums.net/ are a great place to start.
Your goal is to be able to have a fundamental grasp of what you want out of a bike - not just the bike and how it looks, but the riding style you plan to have, and the components you are looking for a bike to have. You should be able to know the difference between an Tourney, Sora, or Ultegra shifter. You should know what frame size you are. You should know whether you want a CroMo, Carbon, or Aluminum fork. Why? Because...
In your price range, you're looking at entry level new bikes purchased online, or used bikes off craigslistIf you know what you want (also check out your local bike shop to ride some different bikes, and try a few things out - you don't even have to buy), you know how to pick through CL ads or online shop for bikes.
-If you understand different components and bike styles, you can make quick yes/no decisions on used Craigslist bikes. Same goes for online bike shopping.
-If you understand basic maintenance, you can assemble a bike bought online or you can tune up a bike off CL that's fallen in a little disrepair.
Most importantly you'll be able to spot a deal! Some people buy bikes and then don't use them, don't know their value, and sell them for far less than they should.
I haven't even gotten to the recommendations yet...why?
I've come to learn bikes aren't one size fits all.What works for others won't be guaranteed to work for you. Take your time with this, or you could find yourself with a empty wallet and a sore back.
So, what do I recommend?
Buyying new? the NashBar Flat Bar is the gold standard of entry level - you don't want a bike with poorer components than this:
http://www.nashbar.com/webapp/wcs/stores/servlet/Product_10053_10052_552047_-1___Used? depends on your area. LIf you can find something like this used, go for it:
https://www.trekbikes.com/us/en_US/bikes/city-bikes/fitness-bikes/fx/fx-2/p/1323010-2017/Two other good online sites:
http://www.bikeshopwarehouse.com/http://bikesdirect.com/As for me? My local CL is devoid of anything good and the LBS near me are out of my price range. I got this:
http://www.breezerbikes.com/archive/2016/liberty-6r on bikeshopwarehouse for $330 shipped. It gets here on Friday.
I barely scratched the surface here. I might update this later if I think of other stuff.
Be careful when shopping used though - bike theft is very common. If it's too goo to be true, it's probably because someone's offloading a stolen bike...