Kagome is also a great choice. Her knowledge of the feudal era and her spiritual powers would make her stand out in Haruhi's world. She could be the one to introduce a sense of mystery and ancient wisdom to the modern and often zany world of the SOS Brigade. Also, seeing how she adapts to Haruhi's world and tries to find a way back to her own while dealing with Haruhi's wild ideas would be really engaging.
One possible interesting plot could be that Haruhi, with her unpredictable and reality - bending nature, somehow stumbles into Kagome's world. Haruhi, being curious and always seeking new things, might start interfering with the normal order of Kagome's quest to defeat demons and retrieve the Shikon Jewel. For example, she could accidentally change some of the rules of the demon world, creating chaos that both she and Kagome have to deal with. This would force Kagome to not only deal with the regular threats but also with Haruhi's unorthodox ways of handling things.
I think Kagome and Kyon would have some interesting exchanges. Kyon is the voice of reason in the SOS Brigade, and Kagome coming from a different world with different rules would challenge his view of things. He might be skeptical of her at first, but as they interact more, he'd start to see that there's more to her world than he thought. And Kagome would be intrigued by Kyon's sarcastic yet practical nature.
Raphael could be really interesting. In the 2003 version, he is hot - tempered and tough. In the 2012 version, he also has a strong personality. Seeing how he reacts to his counterpart and how they might either clash or bond could be a great focus. Maybe they have a friendly rivalry as they compare their fighting skills.
Ross could be really interesting. Since he's an archaeologist, in a crossover with a show like 'Indiana Jones' (in a fanfiction sense), he could go on an adventure with Indiana Jones. Ross would bring his academic knowledge while Indy would have the practical experience. Their interactions would be filled with Ross trying to over - analyze everything and Indy just wanting to get the job done.
Chiaki Nanami could be an excellent choice. She is the Ultimate Gamer, so if you cross her with a digital or virtual world, there are so many possibilities. She could use her gaming skills to navigate through a new digital realm, like a Matrix - like world. Her calm and intelligent nature would also make her a great character to lead the group in a crossover situation. She could figure out the rules of the new world quickly and help the others adapt.
Haruhi Suzumiya herself is extremely interesting. Her boundless energy and her unawareness of her own power make her a complex and engaging character. She is constantly seeking the extraordinary and her actions drive the whole story forward.
Definitely Damon Salvatore. He's the bad - boy vampire with a heart of gold (sometimes). In a crossover, he'd be a wild card. He has his own sense of justice and loyalty, but also a devil - may - care attitude. He could get into all sorts of trouble in the world of the Originals. His sarcastic remarks and his ability to charm his way out of (or into) situations would make for some great scenes. He might also form an unlikely friendship or rivalry with one of the Originals, like Kol perhaps. His backstory and his experiences in 'The Vampire Diaries' would contrast and collide in interesting ways with the Originals' world.
Naruto himself would be very interesting. His energetic and determined personality would make for great adventures in the GTA world. He would probably approach the chaos and crime of GTA with his usual enthusiasm, trying to bring justice in his own ninja - way. His ability to make friends easily could also lead to some interesting alliances with GTA characters.
Ruby would be really interesting. Her energetic and optimistic nature would contrast greatly with the often dark and power - hungry characters in the Overlord world. She could inspire some of the downtrodden minions with her belief in the good of people. Also, her scythe skills and speed would be a unique addition to the battles in the Overlord universe.
Frisk could be a very interesting character to focus on. Frisk has the power of determination, which could be used in unique ways in the FNAF setting. They could befriend some of the animatronics, using their kindness and determination. Also, since Frisk is the player - controlled character in Undertale, it would be interesting to see how they adapt to the more dangerous and unpredictable world of FNAF.