Fortunately that won't be a problem for Zhena. She's really nice, she'll probably be asked if she's Canadian
Awww

Thanks, Laura.
Actually, people over there, especially in tourist places, seem to be very good at picking us out as American. Greetings were generally in English, though a few tried German first. I don't really mind being tagged as American as long as it's not combined with "clueless" or "obnoxious". I can't describe the things that set us apart, but I know they exist. In fact, one time when we needed a little help, we spotted another couple and immediately knew they were American too -- they got us over our little bump.
Getting back to the dress question, I noticed about the same range of variation -- stylish, casual, sloppy, etc. -- that I do in San Francisco. So I didn't make any changes or buy anything special; I just wore what I brought in the same way I would at home.
A few religious sites had posted codes, like no flash, no photos, no food, etc. (I really liked the sign that included a tank top and pair of shorts with the red circle-slash symbol over it). There were always a few people who ignored the codes, except at one site. At the Sultanahmet (Blue) Mosque in Istanbul, they had visitors enter from the side. There they provided plastic bags for shoes (for everyone) and pieces of fabric with velcro (like a sarong) that they handed to every adult, male or female, whose knees were showing. In addition, when we went back a second time later in the afternoon when there were fewer visitors and more opportunity to pay attention, they had other pieces of fabric they handed to women without headcoverings. They collected the bags and fabric at the exits.
I have lots more stories and observations to post, but I probably won't have time until the weekend ... stay tuned.