I'm very sorry to hear about your ill family member. My thoughts are with you.
My family was recently introduced to the details of donor organ waiting lists when my sister's 47 year old brother in law suffered acute liver failure. As with kidneys a living donor transplant is possible when it comes to livers. However we also looked into the possibility of a liver donated postmortem.
We live outside of Boston, which is a major center for transplants. That actually put us at a disadvantage as the ratio of patients waiting for organs relative to donors tends to be high near major transplant centers. As you may know, the country is divided into regions for organ matching. Patients are usually encouraged to register in the region that they live in because if an organ match comes up there is little time to get to the transplant center for the surgery. Some people (e.g. Steve Jobs) have the means to be able to get anywhere quickly and so are able to register in multiple regions, which improves the odds of a match.
I don't know the details of which regions hold out the best odds of a relatively quick match. But I would think you could get a lead from a transplant message board etc. One other possibility - albeit somewhat ethically fraught - would be to consider an overseas transplant. A number of countries have booming 'medical tourism' industries and kidney transplants are offered by many. There are even instances of US insurers footing the bill for their US clients to travel overseas for transplants since the cost of the surgery tends to be lower oversea and in many cases the cost of a transplant and aftercare is lower than that of managing the illnesses caused by failing organs. (I'm not sure how that math works for kidneys as my understanding is that the US government picks up most of the cost of dialysis.)
In the case of my sister's brother in law, he did not recover sufficiently from the initial liver failure to become a serious candidate for a transplant and died after eight weeks.
The official source in the US for donor organ information is http://www.organdonor.gov
and the organization that matches donors and recipients is the United Network for Organ Sharing (UNOS) http://www.unos.org
I wish you and your family all the best. Please keep us posted.