Hello and welcome to the R.T.A. forums.

This is a very popular route and you will find new lots of info on the forums covering the area.

To start out a trip through Death valley is highly recommended as it is a fascinating landscape. You would then generally have 2 options to get around the Sierra's, head North and across the Tioga pass [120] into Yosemite or head South and go around the Sierra's and head for the coast. The main problem is that the Tioga Pass may be closed due to snowfall which removes option 1 if that's the case. These are the closing dates in recent years.
If it is closed and you head around the Southern end you can still visit Yosemite valley and even Sequoia N.P or take the coastal option and drive up the beautiful Pacific coast highway. With 7 days you have plenty of time for the trip and depending on how you want to spend your time could see part of the coast and Yosemite. The Grand Canyon is a 5-6 hour drive from Vegas and would be best done with a stopover for the night. It would be a shame to be that close to such a natural wonder and not see it [unless of course you have been before.] It would also be possible to head to G/C across the Hoover dam and then head to the coast and up to S/F.

This thread has lots of info on the area. Have a look around and when you have more questions, just ask