I'd be mostly up for coop or semi-coop games. Betrayal and asymmetrical are fine too.
Options I know of:
Betrayal at House on the Hill, as described in the OP
Arkham/Eldritch Horror, same
Pandemic, kind of weird. Co-op trying to stop a massive disease outbreak. The gameplay is very abstract and basically comes down to shuffling cards around but somehow it works.
Kingdom Death: As described in OP. Very dense so rough starting out.
Mage Knight: Pseudo-coop RPG-esque game. Demigods invade a fantasy world and work to take it over by friendship or force. You can work together, keep your distance, or even directly attack the other players. Help is nice, but you don't need their help if you steal their shit, and only one player can win at the end. Also very dense.
Various asymmetrical hidden movement games. Fury of Dracula is the most complex, 4v1 hunting dracula. Letters from Whitechapel is 4v1 hunting Jack the Ripper. Specter Ops is 4v1 hunting a spy in a cyberpunk facility.
Catan. My friend really likes Catan, I've never actually played it. I know it has a bit of a reputation, but it's an option.
Those are all the ones I at least semi know how to play.
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I'm pretty iffy on all mafia games. There's one I've seen that seems like it could be good, Mafia de Cuba, but aside from that bluh. MdC has role components in a box and you pass it around, taking components secretly. You know what was in the box when you got it so there's a strong logic element and a basis of (limited) information to start your accusations from.