We stayed at Alfredo's apartment for 10 days and had an absolutely wonderful time. The views from the apartment (and roof terrace) are some of the best on the island. The kitchen works well, the fridge is big, all of which allows for great self-catering in an amazing setting. Alfredo is a very warm, welcoming, and helpful host who speaks good English

The walk up to the apartment from the town is undeniably steep, but just about quick enough not be a problem. A scooter is very handy, and we used taxis (we were charged 20 euro) for late nights eating and drinking in town (although when we did walk at night it felt safe, we were just being lazy!) There's an excellent stone beach - great for swimming - easily accessible from the apartment (1 minute on the scooter followed by a picturesque 10 minute cross-country walk).

Lipari is a very friendly, laid-back island and makes a great base for exploring the other Aeolian islands. You are very close to Vulcano (5 euro on the hydrofoil) which has all its main attractions easily accessible from the port (the crater walk, two great beaches and the Fanghi pools) so logistics are made easy. We explored Salina, Stromboli and Panerea with tours, but again they can be seen independently by hydrofoil from Lipari port.
The views of Vulcano and Etna at sunset from the various viewpoints easily reached by scooter (one 10 minutes from Alfredo's) are among some of the most beautiful sights i have ever seen.
I can't recommend Lipari and the Aeolian islands highly enough for those with a love for natural history and exploration.