As of my last knowledge update in January 2022, here is a list of International Dark Sky Parks in the United States along with suggested times to visit. Please note that this information may change, and it's advisable to check the official websites for the most up-to-date details.

1. Grand Canyon-Parashant National Monument, Arizona:

   • Best Time to Visit: Late spring and early fall are considered ideal due to clear skies and comfortable temperatures.

2. Grand Canyon National Park, Arizona:

   • Best Time to Visit: Similar to Grand Canyon-Parashant, late spring and early fall are recommended for optimal stargazing conditions.

3. Chaco Culture National Historical Park, New Mexico:

   • Best Time to Visit: Spring and fall provide clear skies and pleasant temperatures. Summers can be hot, and winter nights may be chilly.

4. Big Bend National Park, Texas:

   • Best Time to Visit: Winter (November to February) is often preferred for stargazing due to cooler temperatures. Summer nights can be warm.

5. Bryce Canyon National Park, Utah:

   • Best Time to Visit: Summer and early fall are popular for stargazing. However, winter offers the advantage of crisp, clear air and less light pollution.

6. Canyonlands National Park, Utah:

   • Best Time to Visit: Late spring and early fall are recommended for clear skies and comfortable temperatures.

7. Capitol Reef National Park, Utah:

   • Best Time to Visit: Similar to other Utah parks, late spring and early fall are ideal for stargazing.

8. Death Valley National Park, California/Nevada:

   • Best Time to Visit: Winter is the prime time for stargazing due to milder temperatures. Summer nights can be extremely hot.

9. Grand Teton National Park, Wyoming:

   • Best Time to Visit: Late spring and early summer provide clear skies. Fall is also a good time with fewer crowds.

10. Great Basin National Park, Nevada:

    • Best Time to Visit: Summer and early fall are popular for stargazing. The park's high elevation contributes to clear night skies.

11. Hovenweep National Monument, Utah/Colorado:

    • Best Time to Visit: Late spring and early fall are recommended for comfortable temperatures and clear skies.

12. Natural Bridges National Monument, Utah:

    • Best Time to Visit: Similar to other Utah parks, late spring and early fall offer optimal stargazing conditions.

13. Petrified Forest National Park, Arizona:

    • Best Time to Visit: Late spring and early fall are favorable. Summers can be hot during the day.

14. San Juan Island National Historical Park, Washington:

    • Best Time to Visit: Late spring and summer provide pleasant conditions for stargazing.

Before planning a visit, it's advisable to check the official websites of the respective parks or organizations for any updates, events, or changes in the status of their International Dark Sky Park designation.