I'm lucky enough to live in a neighborhod with an inordinate number of churches, and one where (not so much anymore) there was a heavy Eastern European immigrant presence, so I actually live less than a mile from an Eastern Catholic Church building. Funny enough is that there's an Orthodox Church right across the street from it. The EC building is round-shaped. I'd definitely like to visit it.
And ... you should! But, before you go, do some research on that particular rite, so you will know what to expect. Also, in all fairness, once you do attend an Eastern liturgy, you should return 2 more times. As I pointed out to one of the other posters to this thread, the first visit is usually disorienting, the 2nd one brings some sense of familiarity and, by the 3rd visit, you can now begin to fully absorb the liturgy.
I asked to borrow their missalette after attending the liturgy and promised to return it. That gave me more time to read through the prayers, the organization of the liturgy and gain an even deeper appreciation of how they celebrate the Divine Liturgy.
Please let us know how it goes!