Subhan'Allah... The nikah is one of (if not, the) oldest contract that Allah (swt) has estabished between men and women. The Qur'an makes it very clear that Hawwa was there with Adam (as) before they got to Jannah! Allah (swt) gave Adam (as) a wife, before he gave him Jannah! That's something really important to consider.
Anyway, in the interest of getting this sister married, insha'Allah, let's clarify some things.
Firstly, the wali does not actually need to meet the prospective husband in question. The wali's permission is only required for approval of the marriage (i.e. to make the marriage contract). So if he doesn't want to travel to meet the guy, no problem at all.
The sister shouldn't be meeting the guy alone for the sake that it's not appropriate for a man and woman who are not mahrem to one another to be alone together. And for the purpose of marriage, it's better she takes a male (mahrem) with her such that he can guard her interests, because he'll be able to understand better how the guy is thinking and he can give an alternative point of view if they want to discuss the meeting later. Men are generally harder to impress that women, so this advice shouldn't be taken lightly.
The wali can also assign an agent to act on his behalf. If there is someone local that the wali trusts, the wali can permit this person to act in his stead (in terms of waliship, so this person can even approve the marriage contract if need be, as he has this authority from the wali).
If the wali refuses to do this, and is generally acting in an inappropriate or unfair manner, then the sister concerned is able to remove the responsibility of waliship from him and transfer it to someone else of her choosing (especially since she's presumably no longer a virgin, and therefore master of her own affairs). The waliship is a responsibility... it's not a right! If the wali refuses to exercise this responsibility properly and fairly, he loses it! He can't hold the sister to ransom and essentially prevent her from turning down good matches, and effectively never get married.
So in this instance, if the sister wants, she can tell her wali that unless he does something to progress this situation (which is her right), she'll remove waliship from him and transfer it to someone else.
As a side point to note, you will come across many references to the hadith narrated by Aaishah (ra) regarding marriage without a wali being invalid. Whilst this hadith is generally considered authentic, one crucial fact is often missed out. When the scholars of fiqh study hadith, if there is a contradiction between what the narrator of the hadith said, and what they did, the scholars generally follow the actions since the narrator may be acting on further information that they didn't narrate.
Whilst Aaishah appears to have made that statement, she actually did perform a marriage for a sister without the permission of the wali because he wasn't around. When the wali returned, Aaishah (ra) informed the wali that the marriage had happened, and the wali could dissolve the marriage if he had grounds to do so (bear in mind, the Prophet (saw) said not to refuse suitors who have ikhlas and deen). Since the husband was both God-fearing and was strong in his deen, the father had no right to dissolve the marriage, Aaisha (ra) knew this and it was on this basis she performed the marriage (because essentially, if the wali was around, he wouldn't have been able to refuse permission anyway).
And my final point, perfection in speech and advice exists only for Allah, and Allah knows best. Anything correct I have said is from Allah, and any mistake I may have made is from shaytan.
I hope that helps
Assalamu alaykum wa rahmatuLlah
p.s. I would also advise the sister to pay special attention to the family's requirements of compatibility. Whilst she may not agree with the reason, ultimately family acceptance of the husband is crucial for the marriage to be a success. That doesn't mean she should walk away from this prospect, she can still try to convince the family insha'Allah to accept him, and treat their marriage fairly