Hey Will, Big Sur can be an amazing place. I would recommend avoiding Sykes Hot Springs. It has become very well known in recent years and gets a huge amount of traffic. It gets all the traffic while other trails become overgrown due to underuse. On a nice weekend in May there is a strong change of not being able to find a place to camp around Sykes. The hot springs will be crowded. That area can get trashed too.
That time of year I would recommend the trail going from botchers gap campground that heads to the ventana double cone. The entire trail follows a ridge. You get amazing views of the little sure river drainage, the ocean, as well as the ridge connecting kandlbinder and the double cone. You could also hike from botchers gap campground past picco blanco boyscout camp and explore up the little sure river. Be ready to get your feet wet and I hear there are some nice swimming holes and waterfalls to see.
Anywhere you go it’s very important that you check the trail conditions page of the ventana wilderness alliance.
http://www.ventanawild.org/trails/trailconditions.html
It’s possible to get into a lot of trouble if you head up the wrong “trail” without checking, especially if you are planning a loop. Some trails on the map no longer exist.