I think Seth's comment in the previous post was spot-on; at this point, finding ways to integrate systems is important, and connecting encounters and check marks could be a great -- and satisfyingly thematic -- way to do just that.
I'm also mindful of Steve's concern; sometimes, you want to stop in a city that you're "just passing through", and don't want to be encumbered by needing to pay out cards (or else you'd just pay them to get to your destination), but it would still nice to be able to do something beyond simply passing your turn.
I think I have an idea that might address both of these. We know that there are four city types (circle, pentagon, square, and triangle). Assume there are (say) 6 different "sub-location" types -- eg a library, a museum, a hotel, a tomb, etc -- and each city type has 2 or 3 associated sub-locations (eg "circle cities" all have libraries and museums, etc) Each sub-location has an associated deck of encounter cards. AND, each encounter has one or perhaps two different associated "characteristic outcomes", such that if you "pass" the encounter, you will get one of those two things. For example, maybe a "library" gives a check mark; a "hotel" gives a lead to a theme card; a market gives you an ally card, etc. So when you're in a city, even if it's just to kill time, you can still do something potentially productive, but you can also choose what potentially productive thing you want to try to accomplish. And, this could also aid route planning -- if you know you need a clue to the temple location, you might visit a city with a tomb. Etc.
This addresses half of Steve's concern; the other half of it was not needing to pay any adventure cards. Two possible approaches for that; there could be a "do nothing" option that's always available in every city (maybe it's thematically dressed up to be "go to the marketplace" or "go to the consulate", so that your action selection on your turn is always structured as "go to a city and pick a sub-location to visit") -- which could perhaps let you draw a card or look at a lead or something like that.
Another, not necessarily mutually exclusive approach, could be simply that ALL of the encounter cards provide safe passage at the lowest adventure payout, but the "safe passage" will be boring. For example, say you have a stat of 3 in Luck, so you select "Luck 3" for an encounter in which you face an Arab swordsman. Maybe the outcome is that you simply survive the encounter, but you don't get anything interesting for it, either.
A totally different, and again, not necessarily mutually exclusive, option is to have each player have a particular "skill" that connects to the visuals on the cards. I had originally thought this would be a special power, but maybe it's instead that when you see your "trigger" on a card, you get a check mark -- eg, your skill is "languages", so when you see a "book" on an encounter card, you get a check mark in a particular solution category. So this gives you something else interesting to be looking for when you have nothing you especially want to do; you can face an encounter and go fishing for a trigger to your skill.
(Incidentally, another thought -- can check marks be lost?)