Congrats, Diana! I was at Yale earlier this week and had a really good experience. The invite came one week after I was complete, so I guess they must look at the apps as they come in... which doesn't necessarily mean that they won't invite people complete around the same time for an interview later. I flew into Hartford and took Connecticut Limo's bus into New Haven for $34. It took over an hour, and those things have miserable suspension. You can also fly into New York and take a train in. New Haven has an airport but it was super expensive to fly in there.
I can't really think of anything incredibly important that you should know before you go - except take a coat! Everyone has two interviews, and the interviewers are assigned completely randomly. I had one doctor and one student, and they both count the same. Both interviews are open file, and the interviewers know your application pretty well. They're pretty low stress. The adcom meets on Mondays to discuss everyone who interviewed in the last week, but, you know, nonrolling admissions so no news until March. PM me if you have any more questions!