Italy in August is not the best time for a first trip. I know because I live here. If you can delay to the end of August or beginning of September it’s much nicer.
I live near 2 of the 3 main lakes. Where you go depends on your budget and what exactly you want to do.
Lake Maggiore has Stresa, but I would stay further down at Arona. You can still get boats to visit the rest of the lake (right up to Switzerland) and the islands, plus there is a bus to Stresa if you prefer the road route. Stresa is overtouristed IMO, and because of that overpriced. If your budget does stretch to it, stay in one of the Grand Hotels for that Belle Epoque experience. There are lots of charming villages dotted about but whilst some have railway stations, for most you’ll need a car or to use the buses.
Lake Como has Como, also other gems such as Bellagio, Tremezzo, Varenna, plus at the top of the lake there are places like Colico which are more sporty. To get from place to place it’s easier on the boats, or there are buses. Bellagio is a bit like Stresa, super touristy, worth a visit, but probably better not to stay there. As with Maggiore there are lots of pretty places en route, but I’m not entirely sure how accessible on public transport.
Garda has a lot of very different places. I used to sail and surf so only really frequented Riva del Garda and Torbole, which were geared to watersports. However, I had a friend who lived at Limone sul Garda, which was a charming town. Also not far from Verona. At the bottom of the lake is Desenzano, also Sirmione (amazing, but also very touristy - I read they were introducing controls on numbers). Sirmione also has thermal baths and many hotels nearby are geared to this.
For Maggiore and Como the nearest airport is Milan Malpensa, for Garda Verona or Venezia. Although you can also get there from Milan and trains, it’s only about an hour and a half on the fast train to Desenzano, then there are buses to some of the towns. Sorry, not very au fait with the public transport as usually travel by car if not on a direct train line.