2 nights mid to late May

[3hounds]

I know I am late to the game (based on my expected arrival), whereas I have searched through a lot of this forum (thank you!). Yet I'd still appreciate some advice. I love the backcountry and would rather backpack & camp somewhere than stay, let's say, at Curry Village or Upper/Lower Pines (although they are almost completely full). That said, I'm not looking to be the "best at backpacking," yet I do have a lot of experience--in other words 6-7 miles per day is more than enough (only 2 people in our party)--I'm also happy to set up camp once and day hike from there the following day(s). I understand that I won't be able to get into the higher altitudes due to snowpack in mid to late May. I'm also nervous about not getting a backcountry permit at all again, since I'm late the game). I can spend the money on B&Bs, but feel like that takes away from the experience--although it sounds like Yosemite is similar to Grand Central Station, regardless of where you sleep. So with all this confusion and uncertainty, can someone give me a kick in the butt and tell me what I should do. I prefer backpacking, but if you think we should stay in a B&B and only take days hikes, I think I will understand (since this is our first time in Yosemite)...I read Hetchy Hetch and Wawona are the best for backpacking this time of year due to road closures...maybe someone can give me more specifics on that area and what I should do if I'm looking for something rather simple, some solitude, and obviously the ability to experience the grandeur of Yosemite. Thank you in advance for probably answering these questions for the thousandth time!