I've allotted more brain power to this than I probably should have.
So the first thing I did was eliminated all the non-human characters from the possibilities. Especially animals. It might be that Bugs Bunny or Mickey Mouse has a personality that you would find attractive, but it's just too weird to think about everything else that would go with a pairing like that. Also, I obviously ruled out kid characters so no Linus from Peanuts even though he might be a character who has an "old soul."
Next, it was important to me to come up with somebody who did have a personality or that we knew enough about that we could determine how well you might like this person. So, while the Disney princes might all be dreamy, we ultimately don't have a ton of information about most of them. And those we do know more about (say The Beast), nothing really stands out as being all that attractive.
I also factored out some of the more "funny" characters. So no Fred Flintstone, Hagar the Horrible or Beetle Bailey. I also factored out Anime characters at this point, primarily because I don't know anything about that genre.
So then, factoring all that out, what I felt like I was left with from a male cartoon character standpoint were predominantly super heroes. I thought about some of the big name characters like Superman, Batman or Spider-Man and ruled all of them out for various reasons.
Going to the next "tier" of characters, I settled on recommending one of my personal favorite characters of all time, and that is Nightwing. Nightwing is the grown-up version of the original Robin, Dick Grayson. As a young boy, he was a circus performer who saw his parents murdered. Then, he was taken and mentored by Batman and Batman's butler, Alfred. Unlike his mentor, Grayson maintained a social life and close ties to those around him resulting in a much more stable personality than Batman. He is a natural leader and led the "Teen Titans."
Grayson seems to prefer redheads. During his time as Robin, he and Batgirl had a relationship. They went separate ways for a while and for a time, he instead dated and almost married Starfire.
Eventually, he and Batman had a falling out and Grayson relinquished his Robin persona and instead became Nightwing. Eventually reconciling with Batman, he was finally formally adopted by Bruce Wayne making him the official heir to the Wayne fortune and has on at least two occasions been forced to adopt the Batman persona as well.*
Dick Grayson has gone through a few different appearances. Mostly he's been a pretty clean-cut guy, but has gone through a time when he's had longer hair and stubble.
All in all, I'd say Nightwing has it all. Looks, personality, access to money, dependable, and he's good with karate and stuff.
I sent her some links to additional backstory and picture reference. Coincidentally, my friend had worn a black and gray outfit to work recently and I had mentioned she had sort of a Batgirl vibe going with that look. She seemed pleased with the choice. Hopefully she hasn't stumbled onto this site yet.
Parlaying this into a discussion, which cartoon character would you want to date?
* Including currently in the comics. We all know this is finite and that Bruce Wayne will be back as Batman soon.