lol i didn't like her portrayal.
in the books she aint exactly a talkative one... but her character is supposed to be the 'stoic and reserved' type, and not the 'stank faced always angry, dont want shyt to do with anyone' version we saw.
more so, she's one who would actually want to stay in the neighborhood/community they found themselves in.
mind you, i'd feel differently if she were introduced to the governor in the same manner as in the books (in which shyt got real from jump) but given the context in which they've met on the show, it'd be more accurate for her character if she were all about staying. She'd literally the type to say "fukk going back out there... i'm staying here."
I think Michonne being more skeptical of Woodbury and The Governor is a natural reaction for her. She spent a lot of time alone (seemingly her preference) before hooking up with Andrea so she would be a bit less accepting of this situation that looks too good to be true especially when one of the conditions of staying is that she not be allowed to have her sword.