dryerexhaust-ventvent
The house I bought has dryer vent that runs from the dryer into the ceiling. Besides being an eyesore it is also loose/flimsy.
I'm redoing the laundry room and would like to make this more attractive. So far I've thought about enclosing vent in drywall. I'd appreciate any ideas. As a side note, I think it must vent through the roof because I can't find any air movement around the house while the dryer is running.
In general, the shorter the vent, the better, so moving the dryer next to the basement wall would be the optimal solution. If you can't do that, then moving the vent as you said would be a lot better than your current set-up.
This article covers the whole topic in a lot of detail, see especially the sections on why to keep the length as short as possible:
Running the vent to the new location shouldn't be a problem; my preferred tool for cutting the hole would be a hole saw, but they can be expensive. Looking at your photographs, it seems like don't have any plumbing or electrical stuff to complicate the job.
If anyone else has this problem, don't try to take the dryer apart!
I found it's much easier - stick your head in the dryer, and get a good look at the Outlet Grill (Bulkhead Part #32). (If the hyperlink breaks, the Outlet Grill is the part that holds the lint filter). Lint covers up recessed screws on the grill that you need to remove.
Once you get the Outlet Grill off, you have plenty of space to get into the lint duct and clear it out.
Best Answer
Before you do anything, you must figure out where it goes. It really has to vent outside. If it vents into the attic, you are going to have serious issues, including the potential of mold and rot as the hot, moist air is vented into an unconditioned space. It is (usually) against building codes to vent into the attic for this reason.
If it is venting through a roof or soffit vent, or out a wall, you're probably okay. It's best to keep runs as short as possible and with as few bends as possible. Dryer lint building up in the pipe can pose a fire hazard, so the shorter and straighter it is, the less chance there is to have anything build up, and the easier it is to clean out if needed.
Assuming it's vented properly, then I think boxing it in with drywall is a great way to go, and in fact is exactly what I did (in the corner):
You should also consider an in-line lint trap (I probably would have put one in if I knew about them):
I'd also recommend using straight vent pipe where possible, as it is smooth inside which reduces the opportunity for lint to attach and block the pipe. The rigid stuff you have is alright (way better than the white plastic crap) but it is still ridged inside.