For hearthling pilgrimages, of course. They'd basically be player-built quest targets. But unlike the natural ones, they wouldn't be unique, ie there'd be specific types of shrines and going to any shrine of the type required by your quest would complete the objective. The types can be shrines to different gods, natural forces or abstract concepts, depending on where we want to go with the flavor. Shrines should only appear as quest targets for quests given by NPCs within a reasonable radius of a shrine.
The shrines would be a realm object, as their main purpose is to create gathering places for realms' populations. To entice the realms to construct them and leave them open to public, XP rewards for completing quests that involve the shrine should generate twice as much authority as normal XP gain. Also, quests involving a shrine should give XP to the realm even if they're completed outside of the realm. To entice the hermits to complete shrine quests, they should give better rewards on average. The exact rewards bonus could be a subject of competition between realms - ie a realm could invest authority beyond base upkeep into a shrine to increase it's bonus, but this would be measured against other shrines of the same type in the world, and this extra bonus would be awarded from a finite global pool according to relative investments. The idea is that the more authority you pump into your shrine the more visitors you'll get (due to better rewards) and thus generate more authority. However, a bidding war of sorts against other realms could make it unprofitable, which I think creates interesting points for inter-faction politics. Especially if the shrine users couldn't actually tell how much of a bonus it gives, which would make propaganda important.
Shrines could also be required for higher end credo quests (Mystic and Tailor would qualify already). Credo quest would require specific shrines depending on flavor of the quest and the shrine. This could be exploited to further differentiate realms, by making different shrines require different sets of realm policies to function. Of course, you could always quest to another realm to get a credo you really want, but generally it'd be easier to do your realm credos, so populations of different realms would be specialized in different ways. This could also provide long term goals for realms, by locking away some specialist credos behind a set of authority-intensive shrines which require fairly dense population to pay for. Ie something to encourage big open cities like Brodgar.
Finally, it'd be awesome if some of the shrine quests involved slaughtering domestic animals at the shrine.