1. Pierre, South Dakota
2. Santa Fe (2nd is Cheyenne and 3rd is Denver)
3. Honolulu
4. Dover, Delaware; Honolulu, Hawaii; Indianapolis, Indiana; Oklahoma City, Oklahoma
5. Atlanta and Augusta, Baton Rouge and Boise, Pierre and Providence
6. Trenton (borders Pennsylvania), Carson City (California), Juneau (British Columbia)
7. Austin and Boston
8. Augusta, Juneau
9. Annapolis, Boston, Providence, Olympia, Juneau, Honolulu.
(Salt Lake City is a potential trick answer. It doesn't appear on a map to border the Great Salt Lake).
10. Boston
11. Juneau
12. Atlanta
13. Augusta
14. Providence
15. Denver
16. Austin
17. Madison
18. Salem
19. Lincoln
20. Raleigh