Just starting to look into this - Step #1: Pick the collective GB brain...
 
Are there are good Harvest Moon / Sim City games for the iPad out there? One of those games that eats endless hours as you accomplish very little but watching a bunch of numbers tick up.

Depends on how high of quality you want. Tested did an App of the Day on Tiny Tower, that is probably one of the grindiest games ever conceived. The lack of skill or challenge might turn you off. There are some older Final Fantasy games available. The Kairosoft games, such as Game Dev, Mega Mall, Soccer, and Race Car Story are all simply about numbers going up. They might not be that grind focused, but the quality is fairly high. You can play them endlessly or replay for better scores. Games such as Shadow Cities have a large grind MMORPG element. There are also games like Pocket Frogs that play very similar to Farmville. You do lots of repetitive tasks and share resources with friends and level up. The quality is a lot lower here though. If I run across any others I'll stop back and post them here.