I added relevant links...one of which happened to be started by me. Doesn't make it less relevant.
I wouldn't recommend buying new. Not worth it, IMO, especially if you're just commuting around on it. New road bikes
start around $500...not something I'd feel good about leaving locked up in various places where it risks getting stolen. There are tons of bike shops selling used rides in most major cities these days, I'm sure wherever you are moving is no exception.
I still own a car, but I drive it perhaps once every week, maybe once every two weeks. I primarily get around via public transit or bike. I even spent the summer after getting a bike commuting to work on it about 6 1/2 miles each way. I haven't been doing that lately, but if there isn't ice and snow on the road, I generally am on my bike year round to get everywhere else. It's really not very difficult...if you have to grocery shop, get a bike rack and some panniers, or just make smaller trips with a backpack on. There are also grocery delivery services, like Peapod, you can take advantage of.
If you're living in the city you just need to adjust to doing things like grocery shopping more frequently, especially if you lack access to a car where you can buy a couple weeks worth of groceries at a time. But there are lots of car services like Zipcar and iGo that you can take advantage of, otherwise, my bike gets me where I need to go, generally a lot faster that any other mode of transportation.
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