I like non-partisan, nationwide, one-day voting. 24-hour polling stations. No absentee ballots; no early ballots. Top two advance. Four weeks later one nationwide runoff. No electoral college.
This is somewhat reasonable, however absent any serious campaign finance reform having a single nationwide primary day would construe things horribly in favor of monied candidates. For all its flaws, one thing I like about the current primary system is that the tempered pace allows candidates who don't get big donations to still be able to compete (to some extent, anyway).
Scrap primaries. Have an IRV vote between all contenders on election day.
And yes, that includes for President.
This is my ideal preference.
Closed when the parties pay for all expenses of the primary. Open when taxpayer money is involved.
This is sensible if we're maintaining the status quo.