I'm looking for some new manga with a main character much like the ones on Mx0, Zero's Familiar, or Rosario+Vampire, where they stumble into a place where they don't belong, but end up trying to make due and fit in. Or some like To Aru Majutsu No Index, where something stumbles into them. I'd prefer them to be romance and/or comedies, however, some semi-serious ones would be okay as well. Any feedback is appreciated.

If i were you i would read Heart no Kuni no Alice. She stumbles in to Wonderland and ends up trying to fit in. Its been dropped because its been licensed in english, but i dont think that should stop you from reading it though

If you don't mind yuri, then Tokimeki Mononoke Jogakkou?

I've read all of your examples and have enjoyed them...

Maybe try Kandachime, Kaibutsu Oujo, Omamori HImari or even Deadman Wonderland.

All of these have some funny parts and some serious parts. And, I would also second Heart no Kuni no Alice.