More info is needed.

Typically, when I see a basement under a garage, it is at considerable expense meaning that the house has a very large basement that isn't under the garage. The garage portion is closed off with the concrete walls to support the garage precast planks and not open to the larger basement, sometimes deeper, and usually has no windows. So the uses delegated to these large spaces are sports gyms and theatres which coincide with the the way the space is laid out.

I would not list a day bed, nor even risk a room being used as a sleeping room without an emergency escape window.

I'd widen the storage area by a few feet. Depending on the use, you may want shelving for storage and you need room to manuever in front of it. Put the storage area and daybed on the same back wall so you have better open space. You can make narrow builtins around the tv on that whole side wall, where there isn't room for furniture anyway. You might consider using two sofas and a chair instead of a daybed. One could be a sleeper sofa if you have window egress.

I also have a long closet in my finished basement. The previous owners of our house built it out. It may sound crazy, but it's one of my favorite things about the house. I think 5' is the minimum depth. Then you can have shelves that are a foot deep on each wall and have a walkway and room to get things on and off the shelves. We have two doors into our closet, each about five feet from either end. I don't know whether that is better than one wide door, I'm just mentioning it for your consideration. If you know what you plan to store in there that should help you figure out how big to make it and how to place the doors.