I've been a couple of times. It's a fantastic place for a holiday IMO. The climate is great - not too hot or ever really cold. The people really are friendly IMO.
Sadly I can't remember the exact name of the walks we went on but there is a good one that starts at the top cable car station in Funchal. A few of the levada walks are genuinely perilous in places - ie. you slip and you're dead. So you may want to read up on them if either of you haven't got a head for heights. My wife baulked at one of them. Personally I thought they were OK if you were careful. Remember torches if you're doing a tunnel walk. We didn't of course. Because it rises so steeply as you go away from the sea, you can quickly get into clouds, so take waterproofs and warm clothing. Several times we went from hot sun in shorts to totally soaked with drizzle in the space of half and hour's walk. In fact it's so steep that my wife got baro-trauma and lost her hearing from driving up and down the hills. I didn't even know that was possible but I did notice my ears popping.
One interesting little circular one we did was the Soccoridos Valley walk which starts at a big shopping centre to the west of Funchal called Shopping Madeira. So starting in a built up area but within a few minutes you're following a little levada round the back of banana plantations and homesteads and suddenly your on the edge of a very steep valley with waterfalls and then through some tunnels. I thought it was amazing how quickly things changed over short distances.
Get the Walk Madeira book which gives details of 100s of walks but I found the instructions very hard to follow at times and you only get tiny snippets of map. Maps in general seem pretty poor there. Madeira would benefit from the Ordnance Survey taking an interest that's for sure.
I want to go back and not just for walking. I rate Funchal as a town. It's a mix of tourists and working Madeirans. Looks nice and feels real and is very safe. You can pay stupid money for a coffee in a tourist restaurant or walk 2 mins to a tiny bar where locals drink and get one for 50p. Check out the street with the painted doors, the Blandy's Madeira tour, the Santa Clara convent, cable-car, the cruise ships rolling in, take a ride on a wooden sled down the cobbled streets (actually worth the money I thought), the gardens and more.
Elsewhere there are other things to do like the seawater swimming lido place which is great, whale-watching (OK dolphins are more likely), one sandy beach, the Cabo Girau viewing platform (very high) and general beauty everywhere you look.
One thing to bear in mind - use insect repellent 24/7 there and mozzie killer spray in your accomodation. They have Dengue fever there and it's on the rise (apparently a mix of climate change and immigration from Africa - so something there for both Guardian and Mail readers ;-) ) My wife has had Dengue in Thailand and it's no joke - she lost several stone and it can kill. We didn't even know it was there until the way back in the plane when they started spraying the plane with insecticide.