All the most popular trails will have decent access for a stroller. Also, along the main roads in the valley, there are sidewalks that are good for strollers. The views from the sidewalks alone are awesome.
You'll be able to go partially up the mist trail, until you get to the staircase before Vernal Falls. It's worth it. I think you can get to bridal veil falls also. Go to the Yosemite NP website and look at the maps. It's a good resource.
I actually took my 1 year old camping there last summer, and did ok. We camped in the Yosemite Creek campground and it was fun. The creek was mostly dry that time of year. In May, it should be gushing.