2querty: Of the many Breslov leaders today, the vast majority support and encourage travel to Uman for Rosh HaShanah. There are a few who don’t (popular Breslover singer-songwriter Yosef Karduner — check his music out on youtube! — was initially mekareved by one of them, but now believes in going to Uman). Although Rebbe Nachman didn’t leave a “rebbe” as successor, it was clear that Reb Noson was his successor, and since then there have been a group of Breslov gedolim in each generation.
Ivory: Yes, Rebbe Nachman emphasized very strongly the importance of coming to him on Rosh HaShana, and of continuing to visit him after his death.
I’m not sure whether there are any Breslov leaders today who say that *everyone* should try to go. The first thing to do is to study and put into practice Rebbe Nachman’s teachings. If you feel a strong connection to these teachings, and they are a big influence on you, then it may be a good idea for you to go one day.
The only situations in which I think it would be a good idea for a person without a strong connection to Breslov to go is if it would either 1) help strengthen a person who has lost his belief in or enthusiasm for Yiddishkeit, or 2) encourage a person on the path to becoming completely observant. I’ve read of cases of people who had been observant for years but weren’t “feeling it,” but who had an amazing spiritual experience in Uman that greatly improved their subsequent experience with Yiddishkeit (one of the examples I’m thinking of is a woman who visited Uman with a group at a time other than Rosh Hashana).