First of all, I find this thread idea interesting. Pretty much the only character anyone else on this thread so far (that is not from Pokémon) that I even recognized was that last one from Mizz Nikki's post, but oh well. (Nice choice by the way, Mizz Nikki. I would consider that as well.)
For me...Hmmm...I suppose I will put some of my thoughts into two categories below.
Category 1: Fictional characters that I created myself -- Probably most of them actually. I write fiction novels myself, so that is what I am thinking of for this. Sure, a few of them, such as particular antagonists, would go against my own issues with deception / betrayal / similar notions. Many of the rest, however, would be nice. I would really enjoy discussing such topics concerned with their professions.
Category 2: Fictional characters that I did not create myself -- This is definitely more difficult to narrow down for me. From a few television shows to some fictional literature, I could most likely come up with a substantial list. Eh, I do not think doing so would really interest anyone, including me. So...for a notably narrow list, I guess I would appreciate time with the Crane brothers from Frasier...most others from NCIS (thanks, Mizz Nikki) as well. I have not really read much fictional literature lately that has been published in the past … 200 years (or more)? I highly appreciate classic literature from throughout history, but many characters from them may not be the best companions.
No, Hamlet, I would not want to take a tour of Denmark with you, sorry. -- Nor would I want to hang out in your cave, Cyclops from The Odyssey (although perhaps you may want to talk with your father about his reactions to your life circumstances). -- Hey Gilgamesh (*), although you technically did accomplish your immortality goal in one sense, it was not the sense that you spent your time attempting to accomplish. Good effort there, but I would not want to physically search for notably aged people with you when I can just continue my writing and achieve the goal in the same sense that did work. Again, I apologize.
(*) I am certain the version of Gilgamesh from the epic had some differences from any actual version. I am pretty sure any of that second version did not visit the underworld and discuss life with spirits, nor did said version travel long distances, both over land and water, to talk with the only survivor of that cataclysmic flooding. Yeah, as I said, differences.