I stayed at Kogge for two nights with my girlfriend, and we're definitely going to again!
The hotel has 3 S-train stations nearby, and is very easy to find from either of them.
When arriving at the hotel we had to wait a bit for service, but when it (he) finally came, we had a really nice and warm welcome. The chap behind the desk (the hotel bar) were really really friendly and helpful, and made us feel at home immediately. He offered us his own insiders pick on what to see, and told us to come see him if we had any questions. After that, he gave us the key and treated us with a free welcome shot of Jack D.
The hotel overall is quite worn, but actually in a really charming way - they call the place a rock'n'roll hotel, and that's exactly how it felt.
The rooms are all individually decorated, and we got the one called "disco dream". The room was decorated with old LP-covers on the walls and a vintage stereo cabinet serving as a shelf. It looked a bit like everything were about to fall apart, but the atmosphere was nice - it felt like staying in the spare room at your best punkrocker friend's place. It was worn (to put it mildly) but clean and cozy. The only thing missing, was a place to hang your coat and your wet towels - but in return you get free earplugs, to help you deal with the loud music from the bar.
The bathrooms and toilets are shared with the other guests, but since it's a small hotel it isn't a problem - still reasonably clean, and no queuing. The bathrooms are a bit dingy, but when entering the hotel for the first time, you already know that you shouldn't expect spa-treatments.
The bar is the reception as well, and it seemed like a nice place to hang out - nice music and (I think) lots of locals.
Breakfast is from 10-morning till 3 in the afternoon, but we didn't have that (or eat there at all). We checked out the menu though, and it had a nice selection of tex-mex dishes.
On my computers list of access-points, I could see that there is access. I didn't ask for passwords or prices, so I have no clue if they charge extra. It's available though.
As already said, it's really easy to find, and in close proximity to public transport. It is also located in the most buzzing and exiting part of the city - but still sort of retracted from it all. a 5 minute walk, you're in a melting pot of bars, music venues, clubs, hustlers and prostitutes. A 2 minute walk in the opposite direction, and you're at the river Elbe. The hotel is really perfectly located.
Go there for a nice stay on the fringe, but stay out if you're prude. It's not high-class at all, but nice, cheap, perfectly located and with a cozy atmosphere.