Base yourself in Funchal for the whole trip and take one region a day: Funchal and Monte, Pico do Arieiro by car, the east and Machico, the north coast loop, and one flat levada such as Balcões or Levada do Rei. Every highlight here is reachable by car with a short, level walk at the end.
The mistake older visitors make on Madeira is moving hotels. Staying put in Funchal removes packing days, and no part of the island is more than about two hours away by road, so a single base works for a week.
A comfortable week looks like this. Day 1: Funchal old town, the market and the cable car to Monte, with the gardens and a taxi back down. Day 2: drive to Pico do Arieiro — you park at 1,818 m and the first viewpoint is a level 200 m away — then Cabo Girão's glass skywalk, which is step-free. Day 3: the east, with Machico's town beach and the Ponta de São Lourenço viewpoint from the car park rather than the full trail. Day 4: the north-coast loop to Santana, São Vicente and Porto Moniz, all short walks from parking. Day 5: one flat levada. Day 6: Câmara de Lobos and the Funchal promenade. Day 7: gardens and the airport.
For walking, choose Levada dos Balcões (1.5 km each way, flat, no tunnels) or Levada do Rei rather than 25 Fontes or Caldeirão Verde, which involve long unlit tunnels and uneven ground. Avoid the PR1 traverse — it has around 1,000 m of steps and exposed drops.
Practical notes: Funchal's old town is cobbled and steep away from the seafront, hotel transfers with an adapted vehicle need booking ahead, and pharmacies and the private Hospital Particular in Funchal are used to visitors. If mobility is limited rather than simply cautious, the accessible guide has the step-free detail.