For me, a white guy dating a black girl in Southern California, it's been very easy.
I have two grandmothers. grandma #1: she's always been kind of bitter and controlling. We love her no matter what, but since we're children she was always pretty rude to my mom and very strict with us as children. She's still a wonderful person and we love her, she's just old fashion.
Grandma #2: was raised in Kentucky (on an ex-slave plantation) and she's the sweetest grandma you can ask for. The kind that bakes cookies, sews your clothes, and save random things for you the next time she sees you(like a newspaper clipping or a stuffed animal you loved as a kid).
Well, the grandma #1 has turned out to be the absolute most accepting of my girl friend. It's literally like she has not noticed the color of her skin. She's polite, buys her gifts at Christmas, and is as bitter and controlling with her as she is with anyone else.
Grandma #2 has proven different. Since I've been with my girl friend, she's distanced herself from me, called me less, and acts a little odd around my girl friend. She suddenly says "guuurrl" around my girl friend, which is extremely awkward and unusual.
Otherwise, my family is completely accepting of her. They include her in every family event, buy her gifts, support her financially if she needs it, and they spend time with her without me. She is pretty much part of the family. She gets along nauseatingly well with my mom, which is both good and bad (we all know how bad mother in laws can be).
In public I have never experienced anything but positives towards our relationship. The most I've experienced is other white guys congratulating me on having a hot black girl friend. I have to remember I live in Southern California, so I know our relationship would be treated very differently elsewhere.
The worst I deal with is close friends (non of which are white coincidentally) making black jokes or just saying ignorant things about blacks in general. They're used to me finding these things funny, but when you spend so much time with someone of another ethnicity you kind of connect to it. It really bothers me to have close friends say ignorant things, so at this point I tell them not to express those things around me