We have been to Funchal twice and stayed at The Monumental Lido on the main road and at the Eden Mare which is just below the main road nearer to the actual Lido. There are plenty of restaurants in that area. Funchal is a working city and is built up all the way from the harbour and Old town right out to way past the Lido. Which ever area you choose you will find many places to eat. If you scroll back a few pages you will find a thread on Funchal with reccommended restaurants. Be aware that Funchal is on a hill so you may want to use buses (very cheap) or taxis. My mum and dad managed ok and they are both late seventies. If you are going before Christmas the decorations are superb.

Pages three, four and five have Madeira advice.

Funchal is a lovely town and a lovely size to 'get around'. The main shopping area is flat but Madeira is a hilly island ( mountainous even!) so beyond that you may be happier taking taxis or buses.
We stayed out near the Lido. There are plenty of eating/drinking establishments there and also in the old part of Funchal which you would need to reach by taxi as it would probably take about 30 mins by foot. I don't remember taxis being expensive and you could go into Funchal a couple of evenings and stay at the Lido the others.
The vast majority of hotels are out at this end of town. You'll love Madeira. It's a beautiful island and do go on few trips. You'll be amazed by the contrasts in scenery. ( we used strawberrytours & thought they were good)

I worked in Madeira for some years and my daughter (disclaimer here ) works for the Pestana Group of Hotels. I often stay in Pestana Bay which is 4 km from Funchal but it has a free bus service there and back several times a day. Taxi from Funchal to hotel is 5 euros. It also has a swimming pool and of course the usual Pestana quality. Check out its website. Booking can be made by through Atlantic Holidays which are also owned by Pestana. Alsothe Hotel Quarter which is the southwestern side of the island has better weather than others. There are some great little family owned restaurants in the Old Quarter of Funchal and there is a taxi rank there.