Eh, I don't know. It's not a bad idea, but it'd allow you to far too easily to "fortify" a few units in an inn, grab the quest there (and don't complete it) and then rest there whilst attacking an opponent. Then again, that might not be a bad idea on the whole.

Maybe can cost 1 gildar per turn 'fortified' on the inn to pay for room, with the side effect being that you regain hp etc.

If you don't fortify, you don't regen but also don't get charged.

Or every unit pays 1 gold per turn, which means that it can be quite expensive to rest with all of your units.

Having some choices like that would be grand. I know we're not going to get the morality techs GalCiv2 had, but it would still be nice to get some of those sorts of options/events we had thrown at us every so often.

i.e., The innkeeper's wife claims mistreatment at the hands of her husband, and wants you to put an end to him.

Kill him, no questions asked.  (Result might be free rest/fortification here in future as thanks from the wife)
'Recruit' him into your army and take him away. (Free unit, low morale though)
Investigate. (Perhaps find the wife is lying, she is some sort of shapeshifter, the real wife having been murdered recently. Defeating the creature may award some Gil/Item(s)).

I agree. I think, if not just rest, inns should play a larger role than just that of a quest giving hub. It seems a little random to me, which I suppose it ultimately is. Rest, perhaps a place to buy items (including some that might not be available at player cities), or perhaps a place to also recruit heroes.

Then they may not have to just disappear and respawn two squares down after giving a quest, but could have multiple purposes, perhaps becoming integrated into cities expanding into them as a prestige bonus or something...

I like the idea, this way Inns would still service a purpose in the game after quests are completed.