Separate brand on subdomain or different root domain

Hi,

I've got an events venue client that we do general digital marketing for. They are looking at a website redesign which we will be helping them with.

Within a sub-directory they have a page detailing their attached cafe. This was fine at the time but during our initial website redesign chat we came to the conclusion that the cafe really needed to be separated out into it's own thing with it's own branding. During this discussion we suggested maybe setting up the cafe on a subdomain (cafename.venuename.co.uk). The client has asked me to find some examples of this, which has proven difficult as this is quite a specific case and the majority of use cases I've found are more around geographical subdomains or different product lines. Is this still a viable option? Are there any explicit benefits from an SEO perspective for this?

I've also been thinking about suggesting another option; a completely new domain (cafename.london). Would this be more appropriate? I feel that this makes more sense to an end user as a lot of people will just be using the cafe and not the venue, as well as possibly benefits from becoming more 'cafe' focused and ranking better for 'cafe' related keywords.

Appreciate any input I can get on this.

Thanks!