If you want to go in August you need somewhere to stay asap as it's peak holiday season and this year, with so few people travelling abroad, it will be very busy with Italians.
Lipari is the main island, the transport hub and has the most tourist infrastructure. It's a nice island and a good base if you only want to spend a few days in the islands. You could realistically stay there and take day trips to the other ones via hydrofoil.
Stromboli is amazing and you definitely want to see it at night so you can watch the volcanic eruptions. I recommend staying on the island if you can and doing the walk up the volcano with Magmatrek, as it's one of the most amazing things I've ever done in my life. I don't think you can go up to the top any more, as it's considered too dangerous, but seeing the eruptions with your own eyes is truly incredible. You can do it by boat trip if this is your preferred option or if you can't find anywhere to stay.
What is there to do? Mostly, it's walking, a few ruins, there's a museum on Lipari, there's Malvasia wine to taste, black sand beaches, swimming/snorkelling, boat trips, and volcanoes. You can walk around the rim of the one on Vulcano, which also has mud baths you can lounge in and which smell of sulphur. It's a beautiful and other-worldly place! It will be hot though in August.