No specific ideas on safe routes -- will leave that to American contributors with practical local experience.
Just this....
A woman traveling alone without a motor vehicle to lock herself into and blend into the background with, and no "buddy" to watch out for each other -- wow. I'm sure she knows how to be safe but as her dad I wouldn't sleep the whole time. On a 5-day solo trip in Canada's eastern provinces I did meet a young woman at a coffee shop who was coming the other way from Vancouver, and she was almost finished. She'd come from Montreal alone and I think even large chunks of the trip before that were alone, also. I gather she had outlasted a few intermittent male companions who ended up bailing. She didn't look tough or scary (or scared) or anything other than a straightforward sensible young person. I was 50 at the time, and diffident about approaching her to chat, wanting to respect her privacy, but she was quite open to a brief exchange of small talk and route rap before we both had to be off. One eye always on the sun, you know. She didn't volunteer any bad experiences, not that I would have expected her to share vulnerability with a stranger.
The daughter of a friend of mine rode across Canada in company with her female life partner a few years ago. Other than finding themselves sometimes on busy roads with aggressive traffic and no alternative route, they had no scary experiences or even any unwanted discomfiting attention that they saw fit to talk about as being beyond the ordinary crap that women learn they have to deal with. Whether they had more of this on their trip, or less of it, than in their regular "civilian" lives as university students I do not know. They blogged their trip but I cannot find it.
Has your daughter seen this blog site?
Solo Female Cycling Around the World: WOW (Women On Wheels)
The hard part of unsupported solo touring is all the stuff you have to carry on one bike, especially if you are camping. You work hard, really hard. Hoteling it across the continent is prohibitively expensive and in many depopulating rural areas of Canada and the U.S., there may not be any commercial roofs to sleep under anyway...and no cellular service. I can also tell you (and her) that it can be achingly lonely, especially if you are married, which is why I don't do it any more.
As a father, I would make sure she knew that if she found herself out of her depth and wanted to come home, you would pay whatever you could afford to get her on the next bus, plane, train or taxi.