Your players are telling you that they might not want to adventure.
First and foremost, ask your players if this is the case before acting on advice from random strangers on the internet.
It appears to me that they are not interested in playing in an adventure, and that is perfectly fine. There are many other options for the kinds of games to run. The key is not trying to get the characters to be motivated to do something from the outset, but only to make sure the characters have a reason to stay together as a party.
From there you can build on what you already know of the characters. For example, in the homebrew game, it would appear to me that instead of trying to get the largely academic and upper-crust characters to go on a grand adventure, they might have been motivated by courtly intrigue. That is only an example, as it is unclear what kind of plot you actually attempted with that one.
In your Fate game it appears that you tried to start a plot the characters were ill-fit for. A store keeper, a house wife, and a manager are an unlikely group to go gallivanting on a grand investigation, especially when monsters are the order of the day. However, they might have responded to blackmail and underworld pressures.
The point I am making is that if the characters are well thought out, and your players are playing them thoughtfully, the question is not how to motivate the characters to take part in the plot you have planned, but how to plan a plot that fits the existing motivations of the characters.
If you are having trouble finding that plot, ask your players. They are three-quarters of the creative force at your table, after all.
Have a Session 0
Seriously, have a session 0 and discuss what kind of game you're wanting to run versus what kind of game they're wanting to play. There's a clear stylistic mismatch between you and your players, and that should be talked out OoC, not with in-game incentives. No amount of in-game incentives are going to make me want to play Halo when I was expecting League of Legends, and similarly, no amount of in-game incentives is going to stop your players from playing Dark Souls when you're offering them a grinding game.
Best Answer
Give the town unique resources/opportunities.
This may seem callous and calculating, but a town that gives discounts to the adventurers has a special place in the heroes' hearts (and pocketbooks).
Services and opportunities help disguise the ploy a little better; perhaps the town is unusually good at generating cool quests or provides unusually good legal counsel (if that's the kind of game I'm running). I don't need to discount the services if they're superlative or difficult/impossible to come by elsewhere.
Invite the players to help design the town.
I'll ask for their input designing the town, from naming the NPCs and taverns to even tossing them the whole job while I make some tea. (If I'm leaving it all up to them, I consider providing town-generation guidelines from the game book or elsewhere if my players aren't used to this kind of activity.)
This gets players personally invested in the locale, and ensures that it's interesting to them.
Make the PCs guardians of the community.
If the party saves the town as part of a quest, the townsfolk can acknowledge this effusively. Play it up to the PCs' egos: coming to the town means children following them, free drinks, and maybe checking the progress of the statue in their honor.
Make the town memorable for its people, not its stuff.
Elaborate setpieces are cool, but to engage my players with a town I need interesting people in it rather than fancy geography.
Maybe the mayor is an inventor who spends his limited free time (the duties of mayorhood are endless) creating quirky labor-saving devices. Or the whole town is freakishly obsessed with a particular kind of animal, breeding them and hosting regular pet show style contests.
Don't oversaturate.
I shouldn't expect my players to develop intimate connections to every hamlet they run across. I pick one or two locations that we'll be coming back to regularly --preferably they're related to the story at hand, to make it feel more natural-- and focus on them.