The first thing Elizabeth learned about diplomacy after she made it into the State Department was that image is half of everything, and the other half is hard realism. The trick was knowing what to use, and when to use it.
Elizabeth was a realist in private, and an optimist in public.
Take family, for example. Publicly, she loved her parents dearly. She'd like to eventually marry and have children; she just hadn't found the right man yet.
Privately, she realized that she would never have (and more importantly, never wanted) a picket fence and 2.3 children around the same time she concluded that there would never be world peace. Sure, they were both beautiful, fluffy ideals, but she functioned best in a state of mild crisis. Her idea of a crisis didn't involve a screaming toddler (oh, a screaming toddler was a crisis, but not one she would step into voluntarily. Give her the threat of nuclear weapons testing any day).
Simon had wanted a picket fence, but he'd been willing to settle for a dog instead of kids. She probably should have realized sooner than she did that Sedge would only buy her so long. The ending of that relationship had not been unexpected, but the manner had been jarring; it put her off of dating altogether, which wasn't necessarily a bad thing given her position in Atlantis.
Then, for all intents and purposes, her world had ended. Everything she had fought for had been stripped away in the blink of an eye, by a woman whose race Elizabeth had once idolized. That was one image that would never be the same again, and it had been a hard dose of reality. Suddenly, Elizabeth was once again the foreigner, unwelcome in her own home in a way she had not been since returning from her first overseas assignment and finding that her mother had turned her bedroom into storage space.
The first things Elizabeth learned about diplomacy in the Pegasus Galaxy were that possession is 9/10s of the law, everyone is hiding something, and there are times when you shoot first, and ask your questions at the autopsy.
Despite all of that, image still mattered; it was just a different kind of image. Before coming to Atlantis, Elizabeth had negotiated peace treaties and cease-fires; she had never negotiated with kidnappers or terrorists or the fanatically desperate. Each requires a very different game face - different priorities and acceptable losses. Never let it be said that Elizabeth Weir is a slow learner.
She put each and every one of those lessons to use when she established the Alliance of Atlantis, and against all odds the Alliance held fast with Elizabeth as the solitary administrator - neutral and unaffiliated, save to the good of the city. It was an image that was essential, but at its heart it was still only an image.
Publicly, Elizabeth was wedded to Atlantis in every way that mattered. She had given up her home-world, her family, and her people to accept the mantle of Administrator. She was the final authority on actions taken by the largest organized group of humans in the Pegasus Galaxy, and it was enough.
Privately, when doors were closed and lights turned low, she became Elizabeth again for a few brief hours in the arms of her lover. It was what some might call a marriage of convenience, except that marriage had never truly been an option for either of them. She was the Administrator, and he the Chancellor of the Genii - while the political benefits of such a union might be many, the eventual drawbacks would be far greater.
The most important thing that Atlantis taught Elizabeth, and something she all too often forgot, was that lines in the Pegasus Galaxy are drawn in pencil, not in ink. The line between public and private is still just a line, and all lines drawn in pencil will eventually blur.