Is there any way to know how long it will be until a repeatable quest is renewed? Things like the fishing quest or finding Lucas.

Most Quests are 20 hours from the last time you cash them in. Some are 1 Day+20 Hours, fewer are 2 Days+20 Hours, even fewer are 3 Days+20 Hours, and a couple are about a week. Be warned that even though the Fe-Fi_fo_fum Giants Quest and the Share The Wealth Treasure Chest Quest might be 'repeatable' that only means that they could randomly happen at any time and might not for several days.
That 'Quest Log' will tell you everything you need to know about every Quest, both in terms of Time and what you have to do along with what you will or did get.

The Quest log though does lose memory of Quests if they have been inactive for 5 days.

Another thing that's great to know is the Maps 'Show Active Quests' feature. That will tell you where to go to do the various Quests.