I have been twice anon first visit for 9 days, second visit for 4 days.

the best/cheapest way to see it is to hire a vehicle and drive around the islands camping at all the campsites with a tent. Honestly this was a fun experience but you could definitely just get a nice hotel in Torshavn and drive around. I found the Faroe's more similar too the Scottish Highlands/Dingle (Ireland) then Iceland desu. The green mountains in Faroes never fail to disappoint they are absolutely beautiful. If you are the adventurous type hitchhiking is easy and everyone is super friendly. Be aware tolls between tunnels are expensive as fuck.

Its definitely more of a relaxing vibe there, not much happens in the little towns besides the local communities there and it would be hard to get an invite, mos(t maybe all) of them don't even have pubs. The capital is cute though I guess some stuff happens there. If you have any questions let me know as its hard for me to predict what you are into. HIking Sørvágsvatn is a non negotiable keep that in mind (costs 30 franks)