Hey Jameel,
The first thing for you to be aware of is that most of the passes will still be closed in the beginning of April. So other then a long drive around, you pretty much will be committed to the west or the east side of the Sierra.
If you are wanting to see Yosemite, then you should look into flying into Fresno as a first option, or Sacramento. Keep in mind that Yosemite will still probably be a bit brown the first of April. Things will be blooming, but there will not be Dogwood blooms, etc. If you want Yosemite, I would suggest the end of April instead. You will be only able to get into Yosemite Valley, and there is enough to see there for 3 or 4 days easily, but know that Tioga Pass will still be closed so there will be no getting to the High Sierra part of Yosemite. Until these last few storms here I would have predicted an early opening to Tioga Pass (end of May or beginning of June) but now it could easily stay closed until sometime in June.
If it's the Eastern Sierra, then I would suggest flying into Reno, as it gives you a straighter shot down on the East side without having to drive over any passes or deal with issues from any late snow storms too much.
In regards to the Eastern Side, there are some things you won't be able to go see, like the Devils Post Pile as the road to it will still have snow. But Mono Lake will be open, you should be able to get into Bodie. Of course you have the Alabama Hills, the Buttermilks, etc.
If you do the Eastern Sierra, you can start at the north.
Day 1/2 - Do Mono Lake, Bodie, Convict Lake. You can shoot Mono Lake a couple of sunsets or sunrises to get some changes to the clouds for you. I would stay at Murphys Lodge in Lee Vining. If don't camp, that's where I stay, they are inexpensive and nice. Stop by Whoa Nellie Diner, it's a decent place to eat. Some people say it's like the best food west of the Mississippi but for me, the food there is just average, nothing that special. But people will talk about it, so you should go eat there and see for yourself.
Day 3/4 - Switch down to Bishop and there are multitudes of hotels there to choose from. You can go to Alabama Hills, the Buttermilks. Shoot sunset on the Owens River over by Chalk Bluff. There is a lot to just drive around and explore there to find your own unique compositions. Also in Bishop eat at Whisky Creek they have the best Prime Rib. For certain you have to stop in Schat's Bakery. It is the most incredible bakery this side of the Mississippi! No Joke on that. It's awesome. Every time we go up there we have bring back 2 big boxes of Danish's and breads, etc... It's packed usually, but it's worth it. They also make sandwiches inside, so usually we will go and get them to make us a sandwich that we will then take for lunch to eat. Schat's also has a Rib place in Bishop now too, owned by one of the family, and it's got great food there.
That's it for now, hopefully gives you something to think about.