If I had my way, voting for elections on all levels would change to April when taxes are due. Even more detailed, voting would be Thursday through Sunday (6 a.m. to 6 p.m. Thursday thru Saturday and 12 p.m. to 6 p.m. on Sunday). But, like all good ideas for government in this country, it will probably never happen.
So lets look at why Americans vote on the first Tuesday in November:
This was initially established in 1845.
Why early November? For much of our history America was a predominantly agrarian society. Law makers therefore took into account that November was perhaps the most convenient month for farmers and rural workers to be able to travel to the polls. The fall harvest was over, (remembering that spring was planting time and summer was taken up with working the fields and tending the crops) but in the majority of the nation the weather was still mild enough to permit travel over unimproved roads.
Why Tuesday? Since most residents of rural America had to travel a significant distance to the county seat in order to vote, Monday was not considered reasonable as many people would need to begin travel on Sunday. This would, of course, have conflicted with church services and Sunday worship.
Why the first Tuesday after the first Monday? Lawmakers wanted to prevent election day from falling on the first of November for two reasons. November 1st is All Saints Day, a holy day of obligation to Roman Catholics. In addition, most merchants were in the habit of doing their books from the preceding month on the 1st. Congress was apparently worried that the economic success or failure of the previous month might influence the vote of the merchants.
H/T Hendricks County Indiana government website