Well, if I don't want to deal with crowds, I plan a loop in Sequoia/Kings Canyon or in the Sierra National Forest. But that's not what you asked.
A week for someone who is acclimated to the elevation and can do 8-12 miles per day on good trails, I might plan Mono Meadow/Ottoway/Red Peak Pass, and head around through Tuolumne Meadows, perhaps adding a short out and back at the end to Young Lakes and Conness Peak, before ending the trip at Tuolumne Meadows. The only crowded point is TM itself.
A week for someone who is not acclimated, and lives around sea level, I might suggest going to one of the campgrounds (white wolf or tuolumne meadows) for a day or two, doing a short day hike a day, to become better acclimated. The Grand Canyon of the Tuolumne can be 3-5 days depending on how much time you want to spend enjoying the river. You can use the YARTS to shuttle between TM and WW. This might be a good option for you, but it's popular because it's so scenic. The lower elevation end can be really, really hot in summer.
You can put together a week by doing the north rim to Mt Watkins, Tenaya Lake, and around to Clouds Rest then down to Happy Isles. That would mean starting at Rockslides and bouldering a short way with a backpack so you can take the free shuttles back to the car, or thumbing a ride or getting the hiker bus to the Old Big Oak Flat trailhead. Of course, once you get to Clouds Rest, you will be surrounded by day hikers for the rest of the trip.
You could head for Hetch Hetchy, go up the long loop through Jack Main and out through Tiltill to Rancheria, and back to the dam. That would be more remote/less crowded. Though there are spots along the way that were burned out in recent fires, the higher country is gorgeous and worth the effort. Early morning start from the trailhead is a must. There's a lot of exposed and open places to climb. There is a backpacker camp near the parking so you can get the permit on the way in, along with the rented bear canister you must have, and get an early early start the next morning. The road to the dam closes at night, usually at dusk.
You would be better renting a Bearikade by mail from Wild Ideas, if you want to prepack it - highly recommended if you have not packed or used a bear can and have a week of food to get into it -
http://www.adventure-inspired.com/2011/ ... ister.html and trailcooking.com help you understand why this is important. Bear canisters are imperative for any area of Yosemite if 1) you don't want to be fined up to $5000 and/or escorted out of the park and 2) you want to help the bears out by NOT letting them get anything that tastes good from people. Hanging food is illegal and ineffective, and so are Ursacks or bear canisters that are not on Yosemite's approved canister list.
For another thing - always leave a good itinerary with someone trustworthy who will call the appropriate authorities in the event you don't return on time. reconn.org gives you a great template for this. This is a MUST no matter who you go with or how many electric devices you think will work.
Sun protection - it's higher elevation and good polarized glasses, sunscreen, a hat, and even an umbrella can go a long way to preventing a horrible sunburn. People who go into high granite underestimate the power of reflected sun off the crystals in the granite. I always wear breathable long sleeves and long pants - I know shorts and t shirts are comfortable, but the high granite is not what you are used to. A friend who never wears sleeves or long pants burned herself horribly on a trip where we spent hours hiking the open granite - it's also possible to be blinded, and that's not safe especially when you are solo.
Don't forget water treatment. It may look clean, but too many people bring home a souvenir and need antibiotics.