If Rudolf lives, his mother Empress Elisabeth ("Sissi") probably does as well. It was the blow of her son's death, though I understand they were on somewhat strained terms, that chased her out of Vienna more or less for good (except for occasional visits back) and set her on her peregrinations around Europe over the last decade of her life (ironically, she was beginning a return journey to Vienna when she was assassinated in Geneva in September of 1898). With Rudolf alive, she will probably spend a lot more time in the capital, though she'll still do a lot of wandering around the continent, though not to the obsessive degree of OTL.
The status of Franz Ferdinand is also interesting. If Rudolf is still alive and in reasonably good health if and when FF meets Sophie Chotek (I think he still would; I believe Sophie was already working as a lady-in-waiting for Archduchess Isabella at the time of Mayerling OTL - she would have been 20/21 then), then there won't be quite so much pressure on FF to forswear her in favor of a lady with a suitable (Habsburg) bloodline. In that case, the previous speculation is probably right that when Rudolf does die, Franz Josef goes to the next-in-line, Karl. This might mean that Karl and Zita (or whomever Karl marries if he doesn't meet Zita) could become the targets/victims of the Black Hand or other violent radicals. Assuming, of course, that the situation in Serbia develops precisely as it did OTL; the butterflies might have spread far enough by 1905 that King Alexander and Queen Draga (if the two even marry) might survive the coup attempt of that year and "Apis" might end up in front of a bullet-pockmarked wall instead.