(I just added the Arroyo Seco part in the title, realizing that all the things I say about Sykes are relevant to Arroyo Seco as well - crowded, crowded, crowded)
This is a very crowded trail all year long, all week long (Arroyo Seco less so during the winter). It's a relatively easy 10 mile day hike for some people, and is entered through Pfeiffer Big Sur SP, a hotspot for RV's, camping, lodging, etc.
We're working on Quark, but the pit-bull/shepherd in her makes her kind of a guard dog, so we were nervous the first time taking her there. She did fine, but we were extra cautious and kept her close when someone approached. Make sure your dog isn't the type to go off barking and chasing people or other dogs, even if they are friendly.
When you are soaking, the tubs are kind of on a mini-cliff, so it's not easy for your dog to stay close to you, or for you to just jump out and grab them if need be. They are above the Big Sur river so Fido can play in the water, but again, you are not going to be able to have quick access to them, so keep them on a leash in eyesight of the tubs if you're unsure.
Great hike if you don't mind people, nice campgrounds, great soaking (although not so hot as a hot spring should be). More on the Ventana Wilderness and Los Padres National Forest later, it's a great place to take the dogs, and is generally pretty desolate.