Everyone's experience is a little different, as these posts reveal. When you feel the strong urge for a cigarette, just vape harder instead for a few minutes. If that doesn't get rid of the urge, then allow yourself part of a cigarette. But don't trick yourself into believing you need that cigarette. The electronic cigarette is fully capable to provide your body the nicotine it craves. Psychologically it may take longer to convince yourself you no longer want the analogs.
Vaping has some major things going for it that other nicotine-delivery systems don't. Vaping allows one to continue the hand-to-mouth ritual that has become ingrained into our behavior while receiving nicotine. The warm vapor on inhalation and exhalation into our mouth, throat, and lungs comes as close to smoke as you are going to get. That was the downfall of the nicotine patch and gum in my opinion, they couldn't replicate what an e-cigarette can accomplish when compared to smoking an analog.
I had similar issues as yourselves when vaping in public at first. However, the more I did it, the more comfortable I became. I've actually had very few people even take notice of my vaping when out and about. I've used my large and colorful mods everywhere. The people who need to know what they are, do know. I asked the security girl at an outdoor concert would I be allowed for to use my electronic cigarette, and she approved. A security guard at a professional sports event approved of me using them, too.
I've not had any interaction with a police officer, but my ex-wife is a cop and she currently is borrowing my Smokeless Image Volt X2 batteries and clearomizers to try out.
If you are ever in a position to explain what it is (which I find unlikely that you will), honestly say that you are using the electronic cigarette to help you stop smoking. The little information cards are a great way to explain this, if you are uncomfortable to explain it verbally yourself. It helps to explain that it doesn't make smoke, but water vapor.
I've never understood the misconception that people will think you are using an illegal device. Who are these people? How would they know what an illegal device looked like, anyway?
I'd ask them what kind of people do they hang around.
Like many others here, I am proud of myself for having finally quit smoking after 30+ years. I make no attempt to hide this, therefore none of my vaping gear can be mistaken for a cigarette. I do not put myself in that category anymore. I am a former smoker who quit, using an electronic cigarette device.
I actually do not like the label of electronic cigarette, but when explaining it to other people, it is the easiest explanation. I prefer the advanced vaporizer label, but that seems to require much more explanation.