Some years ago my brother went to the USA and wanted to see as many cities as possible during his stay. He purchased a ticket that enabled him to travel on many internal flights and managed to see a lot more than he would have seen if he has driven. He can't remember where he purchased to ticket or what is was called. Is such a thing still available. Any help would be appreciated

They are available occasionally but I haven't seen one marketed by the airlines in about 8 - 10 years. They are usually called a "pass" of some kind, as in "All America Pass" or "See America Pass". The last airline I remember hearing that had it was American back in the 90s.
The only airlines that have something equivalent, but not for the U.S., is Cathay Pacific's All Asia Pass, which they have pretty much every year and Qantas has an Australia / New Zealand pass program. These types of programs have a lot of restrictions and require careful planning to get your money's worth out of them.
Assuming that an "All America" pass program doesn't pop up between now and the time you want to travel, you may want to consider an airline like SouthWest, that flies to pretty much everywhere in the U.S. for usually the lowest price of any carrier and has very frequent flights and doesn't jack the price up sky-high if you want to buy a ticket with relatively short notice (less than 14 days).
Sorry I couldn't point you to anything definitive. Keep in mind also, if you are outside the U.S., there may be programs available to you that I would not hear about because I am inside the U.S. It may be worth your time to do a search on your local Google for "America Air Pass" and see what comes up. You may also want to try your local travel agent, who would be more up-to-date on special programs available in your country.

One more thing - Our national rail service Amtrak has a "See America" pass program usually every summer. Might be another nice option to consider.