I'm sure there is somewhere that you can rent/charter a sailboat on the Chesapeake. Rent one for a weekend, enjoy a Saturday out daysailing and then head back in to the Marina for the night. Tie the dock lines, grab something to eat and then call it a night.
If you find you can't handle it, you're right next to your car and can go home. Personally, I sleep better on a boat than in any landlocked bed I've ever been in. The typical little noises on a boat (creaking, water slapping the hull) are very peaceful, and sleep inducing to most.
The reason I mention going back to the marina is because if you aren't used to it, sitting at anchor might keep you awake all night. I've been sailing for more years than I like to admit, and I never sleep really well at anchor. There are just too many things to go wrong, and Murphy is always a passenger. Why borrow trouble?
As to the claustrophobia, a girl I dated many years ago suffered from that. We spent a night on the boat (at the marina--there was a barbecue and party that night) and when I woke up at 0600, my usual waking hour, she was curled up in a ball in the cockpit, covered with dew. I asked her why and she explained the boat was too confining.
I had her talk to a psyche friend of mine over drinks that week, and my headshrinker friend said, "Just think about this the next time: You're not closed in a tiny place, you're surrounded by something that is keeping the heat, cold and especially the bugs off of you!" She also offered some other tips: don't crawl into that cozy quarter berth. (Cozy being the operative word!) Don't sleep in a sleeping bag. Don't tuck the top sheets or blankets in. Try and pick a place where you'll see more of the boat than just a bulkhead, hull, and overhead when you open your eyes. Don't spend any more time below than you have to. (Boats shrink. After a two week cruise on a 56 footer, I wondered where the last 20 feet of the boat had gone! For someone who doesn't like confined spaces, being below is the worst of all worlds.
Good luck, and I hope you eventually share in the magic of spending your nights at the boat.
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