I live in a Minneapolis suburb. The difficulty with the Twin Cities is that it’s a large metro area surrounding two different cities with a sprawling set of suburbs. We have 50+ parishes and some are up to 90 minutes away from each other. If you want to mention which city/suburb you’re staying in, we could narrow down to something closer to you.
For the entire metro area, here are my suggestions. Although I certainly don’t know all of the parishes, I have been around a lot and have probably attended (at least once) about 20 over the years.
If Latin Mass is your thing, St. Augustine in South St. Paul, St. Agnes in St. Paul, and All Saints (FSSP) in Minneapolis are the mainstays. Rock solid orthodox and very traditional. There are some other very small parishes doing the Latin Mass, but they are mostly in far-flung suburbs.
The St. Paul Cathedral is very orthodox, though not traditional. As the Archbishop’s church, you will not find any heterodoxy there. It also has the best architecture in town - it was based on St. Peter’s Basilica in Rome. I attended there for 10 years and know it well.
I just started attending Holy Family in St. Louis Park. Very orthodox and on the more traditional side. For example, they use the altar rail for communion - the only non-Latin Mass parish I’m aware of that does that here. The current pastor came from a long stint at the Cathedral, so orthodoxy is expected.
One thing to note if you choose Holy Family: the 5pm Sunday Mass and daily 5:30pm Mass is for Anglicans who converted (The Personal Ordinariate of the Chair of St. Peter). I mean, you can go to it, but be aware you might find something different than you expect
There are also parishes you should avoid (based on what you’ve said). I won’t name them, but ask if you find one you’re wondering about.