|Traditional Liturgy at St. Agnes Cathedral in Springfield, Missouri|
Finding a good Catholic Church in your area is probably the most important thing you can do. I'll give some recommendations here. The following only applies to North America.
As a first option, I would recommend trying to connect with an Anglican Ordinariate parish. These are Roman Catholic parishes and communities, in full communion with the Holy See in Rome, but happen to celebrate the Anglican Patrimony. They're usually very traditional and theologically sound (orthodox). They celebrate mass in Sacred English and use elements from the Sarum Use, an ancient liturgy used in England during the late Middle Ages. Any Catholic may become a member of such a parish or community, even if not formally eligible for Ordinariate membership. A map to these parishes, communities, and start-up prayer groups, can be found HERE.
As a second option, I would recommend a parish that celebrates the Traditional Latin Mass (TLM), often called the Extraordinary Form of the Roman Rite (EF), the Tridentine Mass, or the Missal of Pope Pius V. While in Latin, that doesn't mean you won't understand what's going on. A Missal can provide you with English translation, and it doesn't take long to figure out what's going on. Plus the homilies are always in the vernacular language. Now, any Catholic may attend one of these masses no matter what, so long as the mass is being legitimately offered. Probably the best source for cataloguing this is the Coalition In Support of Ecclesia Dei, which can be viewed HERE.
A third option might be an Eastern Catholic Church in full communion with the Holy See of Rome. These parishes are usually liturgically sound and orthodox. In fact, the liturgy they use is often older than anything currently found in the Roman Rite. Any Catholic may attend, and become members of these parishes. However, to become a full-member of the eparchy (eastern equivalent to a diocese), one will have to change rites, which can only be done once per lifetime. Eastern Catholic churches can be found HERE.
As a fourth option, you'll just have to take your chances at a regular Catholic parish. Some of them are quite good, others not so much. There is no way to predict in advance, you can find all of them HERE. I recommend looking for a parish that leans traditionally on the celebration of liturgy, and has a priest who is not afraid to preach what the Church actually teaches on controversial matters like, same-sex "marriage," divorce and "remarriage," and artificial birth control.