There are several decent guidebooks to the area, and the two standouts are:
Rob Casey’s Kayaking Puget Sound & the San Juan Islands: 60 Trips in Northwest Inland Waters, Including the Gulf Islands, 3rd Edition Paperback – May 15, 2012
Randel Washburne’s Kayaking Puget Sound, the San Juans and Gulf Islands: 45 Trips on the Northwest’s Inland Waters (1999)
If you are adventuresome and bring your passport, you can paddle over from the Southern Gulf Islands, and thus avoid a “real” border crossing. You are supposed to check in upon arrival with the US Coast Guard and it’s quite easy and quick, and often a radio call is all that is required. (Check current regulations.)
A better, safer option is driving to Anacortes and either paddling from there, or hopping on a ferry, with your car or just your boat. You can also ferry over and paddle back, or the reverse. The 3 1/2 mile crossing of Rosario Strait (a good hour) must be done in clear and calm weather, as there is lots of large vessel cross traffic. Once over into the San Juans, it’s all quite intimate and safe, with no big crossings and lots of lee shores to hug if winds are high.
The US ferries are a bargain compared with BC’s, and they serve beer! And, all westbound travel is cost free.
For information on walking a kayak onto their ferry system: https://wsdot.wa.gov/travel/washington-state-ferries/rider-information/what-you-can-bring-aboard and https://60tripskayakpugetsound.blogspot.com/2012/01/walking-your-kayak-canoe-or-sup-on.html?m=1 .
The favourite destinations are generally on the northern side of the San Juans, because that’s where the orca, dolphin, and several whale species are usually hanging out: in Boundary Pass. So Sucia and Jones islands are popular, but still quiet. Both are really only accessible by small private boat, although water taxis can get you to either.
If you want to avoid the ferries and not go too far “out on a limb,” Cypress Island, closer to the mainland (just north of Anacortes), is also quiet and pretty.
This is not to say you shouldn’t visit the bigger islands, Orcas, San Juan, Shaw, and Lopez, and even ones as far out as Stuart. There are campgrounds almost everywhere, private and public. Stores and even laundries can be found.