I have never used a hammock, but from the pics I've seen, they look much worse than a tent to me as far as feeling closed in when covered with a tarp.

Take a look at one of our sponsors-Tarptent. Henry (the owner of Tarptent) makes an open designed tent-hence the name. They all get rave reviews and come in different sizes.

Click on the Portal (top of the page) to find the link.

Six Moon Designs also makes a small tent that can be open on one side except in heavy rain when you will want to close it up.

Before getting a hammock, I would take a good look at those.