Mt. Pilatus

I'd suggest going as early as possible, although in August there could be many people that have the same idea of getting an early start. One of the nicest trips (IMO) is to travel by boat from Lucerne to Alpnachstad, and then take the Pilatus Bahn (cogwheel) up the hill. Although the cogwheel funicular runs frequently, that's likely where you'll find a "bottleneck", with people waiting for a seat on the Pilatus Bahn. You could also travel by train to Alpnachstad, but you'd still have the same "bottleneck". For the return trip, take the cable cars down the other side to Kriens, walk down to the main street and take the bus back to Lucerne (only about 15 minutes to Lucerne HBf).

An early morning start would get you to Pilatus in time for lunch. There are two hotels at the top, with the Pilatus Kulm being more posh and formal. The Hotel Aberdeen has a nice buffet, so somewhat less expensive. There was a band playing Swiss music in the Aberdeen dining room when I was there in September, and the crowd was joining in so it was a lively performance.

You may find it less crowded going up by cable car and gondola from Kriens and returning by cog railway to Alpnachstad.

I took the train from Lucerne to Alpnachstad last week and was on the first cogwheel train up the mountain. It was nice to have the place almost to myself for awhile. Things did get crowded later in the morning.

Took the cable car down to Kriens, with a stop in Franmuntegg to ride the toboggan. Nice day.

Note that with a single day, you are prisoner to the weather at the top. See if there's a webcam, and maybe plan an alternate excursion.