@SamanthaJaneSmith Non competitive against each other covers a lot of ground. Many of the co-ops would work (especially something like Pandemic: Hot Zone), or there are things where there's not much interaction and you are doing your own thing without impacting your opponent much, which is the domain of roll and writes or flip and writes. Cartographers is great, or things like Rolling Realms or Railroad Ink (30 Rails is a good *free* alternative)

Sagrada and any of the Ganz Schön Clever range would work too, or Kingdomino/Azul if potentially hate drafting doesn't stretch the non competitive rule too much.

For something a little different you have Dimension or Drop It.

Any of those have a pretty light rules load (the Ganz Schön Clever is probably the trickiest).