The next POTUS will nominate a Supreme Court judge. That is far, far more important than any local issue because Supreme Court decisions have MAJOR impact for the entire country and they supersede any lower-court decisions and invalidate all conflicting laws.
When the Supreme Court says that separating black and white students in public schools is unconstitutional (Brown vs. Board of Education, 1954), it affects you directly.
When the Supreme Court says women have a constitutional right to abortion (Roe v. Wade, 1973), it affects you directly if you're a woman and/or have had your partner need/want to terminate an unwanted pregnancy.
When the Supreme Court says corporations and unions can spend unlimited amounts of money in elections (Citizens United v. Federal Election Commission, 2010), it affects you directly.
Sure, local politicians may affect more day-to-day life matters, but in the grand scheme of things, those don't matter too much. I mean, if you think the amount of budget allocated to the local school system is too little, move to another city/state with a better-funded school system. Not super easy to do, but moving to another country however is considerably more difficult.
To give a concrete example, the current deadlock has stopped Obama's deferred action immigration program, affecting the status of millions of immigrants. It seems likely a Clinton appointee would flip that result, while a Trump appointee would not.
You know Clinton's got this one in the bag, right? It's a done deal. The parties are now just fighting out how bad/good the ass whooping will be.
But to your point... There are local judicial races every year which directly impact your well-being. The players on the the right KNOW that every vote matters, that every race matters, that every inch must be contested, because the system is a giant pyramid.
[1] Specifically, weighted (by sample size) averages of such polls. [2] http://projects.fivethirtyeight.com/2016-election-forecast/
Whereas Clinton has the 2nd most sophisticated operation in history, Trump doesn't have anything that remotely resembles a campaign, much less an effective GOTV effort.
Progressives like me argue that voting for local races and issues, the things that effect you directly, is for more important.
The function of the presidential races is to increase turnout and participation for all that down ballot stuff.