Mt Rushmore - pretty much everyone has seen it in pictures - and it's a top vacation destination in South Dakota. In fact, that's the whole reason it was built/carved - to increase tourism. It does its job well... and it's always fairly crowded (during tourist season anyway). It's "free" to get in, but costs $8 to park - even if you have a National Park Pass. That doesn't sit particularly well with us, but I suppose it's how they guarantee getting money... Expect a short hike from the parking garage to the monument.
We've been there twice now having stopped there two years ago on our first western trip, and then considering it important enough to take my nephew and mom to see it this time. Had my nephew and mom not been with us, we'd have skipped it the second time. However, I do think folks should see it once - esp if they're in the area - mainly because it's so famous.
This trip, we opted to go there from Rapid City's airport after picking my mom up - then took the route through Custer State Park (that's worth doing too - very pretty drive) on our way back to the Badlands (see journal entries for Badlands - don't miss them - everyone we've talked with that have seen both prefer the Badlands - we suggest seeing both).
On your way to the monument from Rapid City you'll pass by several small entertainment options - a typical tourist area. We skipped all those (both times) but stop and see them if you're so inclined. I'm sure they'd appreciate the business. For us, we were just doing a "quickie" on our way out west.
The monument itself is well done - with a nice "Avenue of Flags" (one from each state) leading to it making a nice picture spot from the front. There's a huge gift shop and places to eat. Head down the avenue, and then down the elevator or steps to access the Borglum Museum/studio which gives a great presentation of the history of making the monument - including telling what it was originally supposed to be - and what it ended up being. A visit isn't complete without seeing this aspect of it as the history lesson is quite informative. You can walk below the monument (Presidential Trail - some elevation change with this), but not to the top (surprising some folks).
At night they have lights on the monument - and a ceremony lighting them if you're inclined to stay for that. People that have stayed said they enjoyed it (we left to see Custer State Park before dark). There's lots of great picture spots all over, but in general, you only need to allow 2-3 hours to thoroughly see this place - maybe more if you listen to some of the ranger talks (interesting, but generally restating the same info you can read). Enjoy.