This app was mentioned in 7 comments, with an average of 2.00 upvotes
Whispering Eons #0 has some of that, only that episode out for now, though. Not sure if Noir VR counts also, as it's dialog but not very flexible in terms of being able to pick what you say.
Anyway there are not much daydream apps yet. While cardboard apps are published every day.
E.g. if you like cyberpunk/adventure games: https://play.google.com/store/apps/details?id=com.mick.we.ep0
You can do the above, which sounds like a good idea if you aren't too much "into" it yet... but I have to say that in my limited experience it is key to have a good headset and to try good games (or apps or experiences, but mostly games to be honest) to realize how nice it can be.
This doesn't need to be expensive: my BoboVR Z4 (check out its successor) is fine for immersion, especially with its build-in headphones, which sound good and don't make you fiddle with separate ones (although I am still concerned about its potential health hazards, see relevant thread), and while sadly the number of really great apps is very limited, for some reason, there are a few that definitely show what you can get. My recommendations are:
Generally considered good, although I personally put them in a lower category:
To some extent I agree. But have you tried this: https://play.google.com/store/apps/details?id=com.mick.we.ep0
The adventure genre matches really well with cardboard (IMHO)
Beta is here folks, and it rocks! :-D https://play.google.com/store/apps/details?id=com.mick.we.ep0&hl=en