I decided to do a project where I typed all the percentages (rounded to the tenth) of the vote the republican nominee for president got in all elections from 1856 to 2012 for all states. Some states didn't start until the late 19th century or early 20th century. I finally finished today, and got the averages of all the percentages for the republican candidate. There is a margin of error since I rounded (its probably very small though, so no worries), but here they are:
1. Vermont - 60.2%
2. Kansas - 57.0%
3. Nebraska - 56.2%
4. Wyoming - 55.4%
5. Maine - 54.3%
6. North Dakota - 54.0%
7. Alaska - 53.7%
8. Idaho - 53.6%
8. Utah - 53.6%
10. New Hampshire - 53.2%
11. South Dakota - 52.7%
12. Iowa - 52.1%
13. Michigan - 51.7%
14. Indiana - 51.1%
15. Oklahoma - 50.8%
15. Pennsylvania - 50.8%
17. Ohio - 50.4%
18. Minnesota - 49.7%
18. Wisconsin - 49.7%
20. Connecticut - 49.6%
21. Massachusetts - 49.3%
22. New Jersey - 49.2%
23. Illinois - 49.1%
24. Colorado - 48.6%
24. Rhode Island - 48.6%
26. Arizona - 48.5%
26. West Virginia - 48.5%
28. Oregon - 48.4%
Nationwide - 48.0%29. New Mexico - 47.8%
30. Nevada - 47.2%
30. New York - 47.2%
32. Montana - 47.0%
33. California - 46.6%
34. Washington - 46.4%
35. Delaware - 46.2%
36. Missouri - 45.4%
37. Kentucky - 44.3%
38. Tennessee - 44.1%
39. Maryland - 43.3%
40. North Carolina - 42.7%
41. Virginia - 42.5%
42. Hawaii - 40.6%
43. Florida - 37.8%
44. Arkansas - 37.6%
45. Alabama - 36.0%
46. Texas - 34.8%
47. Louisiana - 32.8%
48. Georgia - 32.7%
49. South Carolina - 31.7%
50. Mississippi - 28.9%
51. District of Columbia - 12.5%
Special Note: If a candidate wasn't on the ballot (ex: Lincoln in the south 1860) it is counted as 0.0%. But if a state didn't hold an election (Confederate States 1864) it is not counted as part of the average.
If you have any requests for certain time periods and certain states averages, I can get the averages off my excel page really easily. I plan to be doing one of these for the democrats too (starting at 1856 as well) and comparing the two sometime in the future.