The comments about Madeira being geared up for the older generation are indeed correct - it's geared up for relaxation and enjoying the sun and the scenery, not clubbing and rowdy beach parties. I was recently out their with my parents and they kept on telling me that and didn't seem to 'get' that (a) I'm 37 so hardly a spring chicken, and (b) some of us don't care for spending a week getting trashed every night. I ended up getting annoyed and was certainly tempted to tell them to cease and desist. :/
Anyway, some advice:
Funchal is good as a centre to explore - plenty of places to eat and drink, but the best bits of Madeira scenery-wise (the locals refer to this as the 'real' Madeira) are outside Funchal. If you're hiring a car, then drive up into the mountains, but if not, then find a local Taxi driver who speaks good English. Once you've found one you like, get their details as in most cases they'll be glad for the repeat business. Most of the drivers will do tours. Half day tours done this way work out at about 50 Euros + tip, which is more than the coach tours but you get to do what you want at your own pace. You can do the same with evening meals outside Funchal (well worth it) - the driver will stay with you for the evening and this will also cost around 50 Euros + tip (excluding the cost of the meal).
You can also take the cablecar up to Mont, which is great for views back down to Funchal and the bay, but pick a day when you can see the top of the mountains, otherwise you'll get clouded out. The temperature (and sometimes weather) difference between Funchal and the mountains is often significant, so go prepared. When you're at the top, the toboggon ride down is fun, but take note it only goes half way down and you'll need to either walk to the bottom (you'd best be fit for that), or get a taxi back up. Both the toboggon and the taxi work out at 20 Euros each.
And finally - most important - watch out for timeshare salesmen. You will get approached - several times. They will offer things like half price tours, which by all means you can take, but be aware you'll have to take a timeshare pitch too. Also, most of the timeshare folks when I was out there were for the Regency Palace hotel, which the locals suggested was in financial trouble.