Hiking, of course! The Yosemite Falls Trail is one of the most popular and generally open this time of year. Bridal Falls is lovely, and you can walk up to the bottom of the falls.
Don't miss having a meal at the Ahwahnee Hotel - it's a beautiful building with a great restaurant. If the prices are a little steep, go to the bar, get a drink, and relax by one of the huge stone fireplaces.
Bring binoculars for night sky viewing on moonless nights.
Quick Tips:
Spring is a good time to visit - the weather is often gorgeous and the park is not as crowded as it can be in the summer.
,
Many of the hiking trails are closed for the season, but depending on the weather, there are still plenty of trails to explore.
Make sure you have tire chains for your car - the rangers can turn you around at the park entrance if you don't have them.
Best Way To Get Around:
Hiking, of course! Even walking along the road on the valley floor you get incredible views of the falls, meadows, and cliffs. I've often seen deer and coyotes from, or even on, the roads.
Bicycling along the valley roads is also easy, as the floor is completely flat along the roads and lovely.
If you want to get somewhere a little quicker, the shuttle buses have a route along the valley floor. Visit the visitor center for a map of the shuttle stops.