What island are you going to? How long?
Assuming you're going to Santa Cruz, there is the ability to do an overnight trip from prisoner's harbor to scorpion anchorage. You are pretty restricted on where you can camp though... Just the del norte camp out by prisoners or the campground in scorpion anchorage. I'm not sure of the trail conditions at the moment; you should probably check with the park service folks. Other than in the campgrounds at scorpion, water is very unreliable on the island. Plan to have to pack in all you need if you end up trying the hike from prisoners to scorpion.
If you go to prisoners, there is a beautiful but short day hike on the nature conservancy side of the island from prisoners to pelican bay. It's the only part of the nature conservancy half of the island open to the public. You may need an island packers escort though. Otherwise, other nice hikes are out to the potato harbor lookout out towards coche point or out to smugglers harbor. There's a really pretty bay out past smugglers, called yellow banks. There used to be a trail to it, not sure any more... If the sea conditions/tide are cooperating, it's quicker to walk the beach at smugglers and climb up and over the rocky headland at the far end to reach yellow banks. It's a bit of a rock hop and some scrambling but you're rewarded with a big beautiful sandy beach to yourself without other hikers. SCI is great for kayaking around scorpion anchorage. Lots of sea caves to explore.
If you go to anacapa island, there's just one campground. It's a very small island, more like a big rock... You can walk it all in an afternoon. It's a better island to visit for a day or to use as a base camp for kayaking or scuba diving.
Santa Rosa island is a bit harder to get to but really nice. There are some options for backpacking style trips on this island but it gets tricky to plan because of the limited number of trips offered to the island and various seasonal closures of parts of the island due to endangered bird species, huge marine mammals occupying some of the beaches and a private deer hunting concession. You would need to do a bit of research and consult with the folks at NPS to see if there are any feasible options for backpacking trips on SRI right now. Otherwise, you've got to stay in the main walk- in campground. Nice hikes are out to the Torrey pines or out towards skunk point or east point if you have the time.
Finally, on San miguel island, you are very restricted and all hikes must be done with ranger guide due to the very sensitive resources on the island. This island is very remote and very windy. It's a long boat trip out there but you're rewarded with empty windswept vistas, intact archaeological sites, amazing sea life and a chance to be on one of the least visited NPS owned properties in the country.
Keep an eye out for gray whales on you boat rides to/from the island. The gray whales pass through the Santa Barbara channel and many are on their way back up from baja right now with their calves.
Let me know if you want any more info on a particular island; i've spent some time on all of them.