As long as it is a place where I have to be (school, work) etc I'm fine with staying silent. Nothing else even enters my mind. If I don't have anything to say, I won't say anything, if I have something to say, I'll say it. Those silences aren't awkward or uncomfortable for me. I'll just do whatever I'm supposed to be doing, or read or listen to MP3 or just be in my own world.
I'm pretty much only in a car if I I'm riding with my mother or taking a taxi (very rarely), and silences with my mother aren't awkward. In taxis I don't feel any obligation to be talkative, I'll just follow the driver's lead, or keep stand-offish if I don't feel like talking.
For me silences only get awkward in actual social situations (when I'm trying to talk to someone).