We are thinking about visiting Brice and the surrounding parks in June. Is that a good time? Are there long lines or parking problems?

It's a good time to visiting Bryce national Park. No parking problems.

There is no bad time to visit Bryce Canyon. Just go and take it all in.

The park will be busy, but not so much to ruin your visit. Parking, when I've been there in June, was not too hard to find. Even in early June there can be cool temps. I've even encountered snow flurries. Check the forecast and be prepared.