There’s nothing wrong with exploring the other Rites in the Catholic Church. Going to Mass in another Rite satisfies your Sunday obligation. If you want to receive Communion, you may want to talk to the priest about it first. (A lot of Rites like to make sure you’ve gone to Confession before you receive Communion, or that you’re not a non-Catholic rubbernecker who doesn’t know better. They often have small congregations, so the priest knows everybody and who’s gone to Confession.)
If you end up really becoming attached, you can even change Rites (although usually it’s not necessary unless you want to get ordained in that Rite, or something similarly big).
If there’s a Lebanese Christian community in your area, there’s probably a Maronite Catholic church. If Iraqi or Syrian Christians are around, look for Syriac or Chaldean Catholics. If there are Greeks, Eastern Europeans, or people from Asia Minor, there may be a Byzantine Catholic or Ruthenian Catholic church.
There are a ton of Rites, but these are pretty common ones to find in the US. When it gets to be Christmastime or summer church festival time, a lot of local Catholic churches hold open house. It’s a good time to visit and ask questions about other Rites. (And you can buy some darned good food at church festivals and bazaars!) But of course you can also just drop in for Mass, as I said above.
Also, you might just find that other ethnic groups have Latin Rite Catholic parishes with customs or devotional practices that you might find more helpful to your growth as a Christian. Vietnamese parishes sing beautiful Vietnamese-French chant, for example. Everybody says it’s great to go say the Rosary in a Hispanic parish at Our Lady of Guadelupe Mananitas services. And so on.
The Church is full of good and holy things. There’s nothing wrong with exploring that wealth and meeting your neighbors.