We stayed in Funchal on our second trip to Madeira and would defititely reccomend staying in this area if you like to be in a lively area with restaurants, cafes and bars. There's lots of beautiful apartments with ocean views that are mid-range. It's slightly more expensive to stay in Funchal just because of the location, but its worth it to be close to shops and places to eat.

The Fort of Old Town Apartments by OurMadeira offer plenty of modern apartments around Funchal with sea views and mid-range pricing.