Really? A multi-day kayak trip with no camping? What's your aversion to tents? Do you need someone to do the paddling for you, too? And to find a way to make sure you don't get wet? The whole point of a backcountry paddling trip is that it takes you far away from civilization—to places you can only see and experience by boat. Setting up camp for the night on some primitive shoreline site is part of the experience. That's why expedition kayaks come with those huge storage compartments.
Yes, there are a small handful of established inn-to-inn trips in the States you can take (and they're quite nice), but none of note lie within the Mid-Atlantic. So I'll respond to your question in two parts. The first is a rundown of great paddling expedition options in the Mid-Atlantic that will force you to brave the starlight and fresh air by sleeping outdoors. The second describes a few of the country's top inn-to-inn multi-day kayaking expeditions.
The region is packed with great water trails—mostly on flat, slow-moving rivers that eventually drain into the Chesapeake Bay. For that reason, your best initial resource on kayaking routes is the Chesapeake Bay Gateways Network. Its water trails map, is quite extensive—covering an area that runs from Upstate New York down to southern Virginia near the North Carolina border—and provides brief but useful descriptions. The four premier water trails are located on the Susquehanna River. For detailed information check out the Pennsylvania Fish and Boat Commission. But suffice it to say that the 450-mile Susquehanna (including its two upriver branches), form the largest waterway devoid of commercial boat traffic in the country. I'd suggest the 51-mile Middle Section, from Sunbury to Harrisburg. The route is largely undeveloped and wild, with only the occasional reminder that you're only a short distance removed from the sprawling East Coast megalopolis. There are 22 primitive campsites on 20 islands along this stretch.
You've essentially got two choices: the Maine coast or the San Juan Islands of Washington—and you'll definitely need the help of an outfitter to plan the trip properly. Maine Kayak organizes two-day ($380 per person) and four-day ($960) expeditions just northeast of Portland around Linekin Bay and Boothbay Harbor, with overnights at coastal bed and breakfasts along the way. Water Walker leads three-day trips ($270 per person), operating a short distance further north, among the rocky islands around Tenants Harbor and into West Penobscot Bay.
In the San Juans, Crystal Seas Kayaking puts together inn-to-inn trips that vary in length from two days ($880 per person) to six ($2,380 per person), through Orcas, Lopez, and San Juan islands in Puget Sound. Along with paddling among the whales and porpoises, and spotting bald eagles among the stark, Douglas fir-garnished islands in Puget Sound, you'll be eating at some of the region's top restaurants and staying at high-end inns.