She could be out on the Appalachian Trail getting on it from NJ while wearing a balaclava-type face covering for 'sun/weather protection' where she'd be unrecognizable and around very few people while not looking suspicious. Also she could go into stores intermittently along the trail with her full face covered with her being a hiker making a re-supply stop where it wouldn't even raise an eyebrow with it just being another hiker.
In Western WA, most people still wear masks outside. If someone doesn’t, it is probably OK, but if someone does, it won’t be surprising.
In terms of where to hide without leaving the country, I’d say the northern parts of both coasts are surprisingly good.
In North England, the type of living on a decent parcel of land, with trees, in an old barn converted into the house, especially if working from the home, has gained popularity a while ago. This is when the neighbors will never notice if one of them got a new girlfriend, because they are, truly, uncurious, and people around are physically unseen. To notice that the amount of mail deliveries has doubled or tripled is of no interest to anyone. The only problem might emerge if the GF has acute appendicitis, but if she is young and healthy, she can live in such an environment for years.
Ironically, huge cities with big transportation system, such as NY or Boston, can be great places to hide, were it not for bureaucratic operations related to finding an apartment to live in. But the sheer amount of people makes your invisible; also, huge student populations with their share of very young, very pretty, girls, makes one of 34 stand out less. As long as she hides the hair.
So, an old BF or slightly older, lonely dude living on a sizable acreage in US Northeast. My bet nr 1.
Edited to add: Jaymie Closs abduction would have remained unsolved were it not for Jaymie herself, but the answer to how it became possible is in two words: “rural Wisconsin”. One doesn’t even need a huge acreage. And Wisconsin is decently populated as opposed to MN, VT or even NH. So, looking at the population density map, I’d add MT or Wyoming to NE states. The Dakotas are OK, too, but the oil boom drew in a lot of single guys, any woman becomes noticeable in such conditions. Didn’t KA grow up in MN or something like it? She probably won’t stay in own state (or a school BF who is unmarried and lives on own land is not impossible, but still, too risky). But what she might know well would be the mentality of the people and how to not get bored living there.
There are some things a woman might still need. Should purchase of some extra meds by some of her old friends or family be the sign?