How do you get it there? Hopefully this thought occurred to you. And if not, maybe I'll save you a little embarrassment (though there is no reason to be embarrassed by a lack of knowledge).
What's the problem? Carrying between public and private "domains" is prohibited on Shabbat. This is halacha d'oraisa, which means it is from the Written Law of the Torah. It's more serious than a rabbinic prohibition.
Of course, this law only applies to halachic Jews. If you're a Jew who doesn't keep kosher, you're probably not bothered by this issue. If you haven't converted or have "only" a Jewish father, you are also not held to this law. However, there is something to be said for fitting in and "doing as the Romans do." You might also want to avoid bringing any attention to your status from other guests or congregants. (Remember that your host NEEDS TO KNOW if you are not halachically Jewish.)
So how do you get your food/drink item from your house to your gracious host's home? There are two possibilities, and they all revolve around whether there is an eruv in the community that encompasses both homes. Note that you must check whether the eruv is "up" for the coming Shabbat.
If there is an eruv: You can carry the item with you. Most likely, you will carry it to synagogue with you and then to your host's home. It's fine to carry it in a bag or whatever you need to do to carry it comfortably. (Probably not by riding an electric scooter.)
If there is not an eruv OR the eruv is "down": Carry/drive/teleport the item to your host's home BEFORE Shabbat begins. If you drive, etc, be careful that you leave enough time to get back home or to the synagogue before Shabbat begins. If you are worried about being seen carrying on Shabbat, you probably don't want to be seen driving on Shabbat either. (You might be able to leave your car at your host's home, especially if there is on-street/public parking.)