Hi Anna, we too are glad you found us, welcome to the RTA forums !
Your proposed trip is very doable and to be honest, a very relaxed affair compared to some 'opening 10 day itinerarys.
All your goals are comfortably within a days drive of each other, so it's a case of working out how long you would like to spend where and see if you have a little 'wiggle' room for other attractions. You say you have been to the west coast before [a few times by the sounds of things] so there might be places you want to re-visit or places new to be found.
To fit in with your current plans, Death Valley, Joshua Tree NP, Route 66 towns like Oatman, The Mojave National Preserve and Hoover Dam are a few of the nearby locations to your route. Just north of Vegas is Valley of Fire State park and further north, Zion NP. If you looked further afield you have Sequoia NP, possibly Yosemite, the PCH and even the Grand canyon to consider.
You will find a lot of info around the forums to help you decide and then we can help fill in the blanks. If you are aiming for more of a City break that's fine, but otherwise I would try and balance your trip out with a few natural wonders. It's easy to spend a few days in each of Vegas, LA and SD and leave little time for much else.