I like games that you can take your own approach to play so I wanted to pitch this as an idea:
All properties will be unlocked the moment after you beat the tutorial excluding the museum as that's your ultimate goal (you can get into the museum but you can't get into the attic, you know what i mean) however you may ask how would this make the game non linear well I have some solutions to it
Every property you successfully get the key from, it will count as a day and the night sequence will begin (or just have day and night slowly transitioning and the day/night achievements will be instead tied to you beating the properties in your own order.) what i mean by this is that you could beat the Mayor's property on Day 1 and then you'd be put into Night 1. etc
Have each property need something from another residence, if something's blocked off in the bakery, i doubt Gerda will have a crowbar lying around so you'd have to head back to let's say the old neighbor's house to get one. Some of these will be replacements for puzzles and others can just be for side quests, like digging up a container of golden apple coins at the museum.
If the player has no idea where to go, the game will point you in the direction of the 'recommended' property to start off at. You could start off at the bakery and get something to eat but the game would hint that you should go to the police station after the tutorial is over.
Another good way to point that you're making progress is bring back the little watch notification and have it refer you back to the pinboard, yes, I think the pinboard should get more usage and be updated as you continue the game. The only problem was in the beta it didn't indicate that it was the pinboard being updated.
If the dev team is afraid of all the walking getting annoying, then allow for the player to use Quentin's bike to easily navigate around outside, it'd be faster than sprinting and perhaps could have a system where Quentin can retrieve his bike if it gets stuck somewhere.
I'm just a fan of non-linear games, and the beta was an alright non-linear experience I just wish we got what was in it.
As a update since the halloween update came out, I'd say it'd be better for the forest section to be not available until you beat Mr. Peterson at least until the story gets properly continued. It just feels a bit odd how right after the tutorial you just can run straight into the forest.
