I've just reached level 9 and I'm getting a bit frustrated with the sleeping situation in Fallout 3.
Playing as this lone wanderer it seems realistic that I don't have a permanent place to live and sleep but being extremely low on health and money right now makes me want to find a place I can fast travel to and have a nap for a couple of hours. Having a workbench there would be nice too.

I have heard of the apartment in Tenpenny Tower you can claim if you blow up a certain small town.
I did not do that, however I took a key off the body of a dead former inhabitant of this tower. Can I take over his apartment? If so, where can I find Tenpenny Tower?

Any other suggestions on finding a place to stay without spoiling too much would be greatly appreciated.

Did you do the bomb quest in Megaton?

If i'm not mistaken you can also get a house or sleeping loc. inside Megatron, but if you are on the evil side. I suggest blowing up the town, you'll get quite the spectacle and a free apartment aswell ;)

Disarm the bomb and the sheriff of Megaton will give you a house. Blow up the bomb and what's his face will give you a suite.

The sheriff is dead and I took the key from the guy offering me to help him blow up Megaton. He is also dead now :)
I really don't want to disarm the bomb to not offend the religious nutjobs in Megaton.
Where is Tenpenny Tower located relative to Megaton?

West-Southwest.

Edit: Even if the Sheriff is dead you can still disarm the bomb and his son will give you the key. Disarming the bomb has no effect on the followers of Atom or whatever.

Ah great! Thanks for the info PureRok!

You could always shiv someone and live in their house.

plus when you disarm the bomb (which is what i did) your pad can be customized with Moira brown, to fit any need you have.  vault theme or pre war theme...etc... workbenches and mini clinics, its great but at level 9 I'd suggest not spending the money if your maintaining everything else ok.  Also, take advantage of the storage area in your home.  Don't carry weapons or armor, or even simple things like misc. objects that you dont need at the moment.  Keep your weight down so you can grab good stuff on future missions.

To be fair, the tenpenny tower apartment has all of the same perks as the one in megaton. essentially, as long as you do something with the bomb, you'll earn a living situation.

The tenpenny tower one also involves alot more travel to get to it with going up the elavator etc.

I'd advise the Megaton House, unless you really like fresh water and jokes about catholic neutrons.

"The tenpenny tower one also involves alot more travel to get to it with going up the elavator etc."

Oh id just kill all the ghouls if i were you get a follower to help you go to evergreen mills and buy the shotgun they get a damage bonus against ghouls