Here are some Yosemite options. Some people will complain about the crowds and how they are too good for Yosemite Valley and blah blah blah. IMO everyone needs to visit Yosemite at least once in their lives. The waterfalls are truly breathtaking! The farther back you hike the fewer people you'll see.
1. Mist Trail (7 miles, 2,000 AEG) - This hike takes you past Vernal Falls and Nevada Falls. This is also the lower portion of the Half Dome hike. It's the most popular hike in the park. You hike along the Merced River as you gain elevation to the top of both waterfalls. I love this hike and have done it four separate times.
2. Upper Yosemite Falls (9 miles, 3,000 AEG) - This is another popular hike. You gain a lot of elevation as you work your way up the trail. There are a bunch of spectacular views of the falls as well as Half Dome and Yosemite Valley. I recommend heading all the way up to Yosemite Point. It's roughly a mile past the top of the falls and well worth it! http://hikearizona.com/photoset.php?ID=11397
3. Lower Yosemite Falls (Less then 1 mile and its paved) - If your in the area and have time, make a quick detour over to the lower portion. Bridalveil Falls are similar with length and time.
4. Glacier Point - Absolutely spectacular views! This is possibly my favorite place on earth. You can hike up from the valley floor (Four Mile Trail or Pohono Trail) or drive your car. It's worth the time getting there. http://hikearizona.com/photo.php?ZIP=198832
Try to hike over to Sentinel Dome if you drive. It's a short 2 mile round trip hike from the road.
5. Some sites to check out if you can...Olmsted Point, Tunnel View, Ahwahnee Hotel and Mariposa Grove. Mariposa Grove has the giant trees you mentioned in your post.