This is where we stayed in Funchal. Was lovely! https://www.quintasantaluzia.com/
Will you have a car? It makes exploring so much easier (but get one with a decent amount of power to get you up the hills).
I can't recommend this place highly enough https://fajadospadres.com/faja/
It's a working farm, growing all sort of tropical fruit and veg, and is primarily a restaurant. You can only access it by cable car. You can either spend the day, having a long lazy lunch (I still remeber the incredible octopus, and huge jug of white Sangria) and sitting on the beach, or you can stay overnight in the little cottages there. We stayed 2 nights and it was a highlight of our trip. 1 night would be enough, but we had 11 days on the island so were taking things at a leisurely pace.
Other highlights were a food tour in Funchal, a trip to the Valley of the Nuns, the sea pools at Porto Monitz, the amazing mountain scenery in general, a trip to the very eastern tip of the island.
Personally I think a day or 2 in Funchal itself is enough, and I'd split your time and stay somewhere else too - somewhere further west, like Calheta perhaps. Means you have easier access to all the things there are to see. But then I never spend a whole week in one place, and I realise that moving around isn't for everyone!
I don't quite know why it has a reputation for attracting an older crowd (you'll feel young in Funchal!). Outside of Funchal we noticed it less, but the average age of tourists was definitely more than elsewhere in Europe. I'm glad we didn't stay in a big hotel, for that reason.
I'd go back in a flash though - amazing holiday destination.