When visiting tourist sites, how you get in is just as critical in saving time as getting there. First major tip I can give is to find alternative entrances other than the main entrance. Major sites typically have multiple entrances and multiple ticket offices but most people are only aware of the main entrance. The alternate entrances aren’t posted but if you walk around, you’ll find them. For example, the main entrance to the Louvre is beneath the glass pyramid and the long line that forms outside is for people waiting to buy a ticket to get to the line to get inside (yes the first of 2 lines). However, there are 2 separate entrances off to the side and hidden in a small corridor (flanked by 2 large lion statues). You can walk in, buy a ticket, and bypass the entire line at the main entrance.
Some sites have lines for cash vs. credit card. If you don’t care, get in the shorter one. Sometimes, the line will split in two each able to handle customers but large groups will typically stay together so the separate line won’t be utilized. If you’re behind a large group, try walking up to the front to see if they’re all waiting go through the same turnstile. If so, politely ask to go around to the other side.
Of course I say all this with the regards to the line. I’m not advocating just storming to the front of the line with absolutely disregard for those in front. I’m not an animal. But I am saying it never hurts to figure out the easiest and quickest way to get in especially if there are lines being underutilized.