We also stayed at DGI-Byen over the New Year period. My main reason for booking this hotel was for the swimming and spa facilities which unfortunately were closed on the 31/12 and 1/1. If I had known this when booking I would have booked elsewhere.

Good points

Close to train station and Tivoli
Breakfast was fine
Helpful staff
Clean rooms
Access to internet in lobby

Not so good points

Facilities not open (although this was because of the holidays)
Double bed not a double but 2 singles pushed together
The cups with tea and coffee were polystyrene!

Would try somewhere else in Copenhagen next time

My partner and I spent 5 nights at the DGI Byen for New Year's. The hotel is very much centrally located next to the train station. The area used to be rough, but there are some nice pubs around.
DGI Byen is part of a big meeting-sports-hotel centre. Roms are very spacious. Bathroom are nice sized. However we had a few problems. For some reason the cleaners would not clean every morning. We had some real problems with the temperature of the water. Shower was sometimes really cold. We asked the reception and the plumber fixed, however the problem remained.
Double bed is not double. DGI' s double bed, though, has seperate small duvets as well, which doesnt give much room for cuddling.
Our weirdest experience was with the sports centre. Although, it was probably one of the largest sports-pool centre in Copenhagen it lacks proper management. It was closed on the 31st and Jan 1st, which meant that we had nothing to do those days. Also, when we actually decided to use the (complimentary for hotel guests) spa we were asked to pay 10 pounds each. I know that this is not that much, however they decided to designate that price at the beginning of New Year.
We of course asked this money back from the hotel and they were kind enough to give them back.
As a whole the experience was very average. And guests, beware, the sports centre is open to the public, so it ;s not as relaxing as you would have thought.

Had booked this hotel then found the online reviews in trip advisor so I was very very afraid. However it was okay, the location whilst not pretty was very convenient walking distance from Central Station (though trains were noisy through the night) and an easy walk up to Vesterbro for reasonably priced (by Danish standard) meals, and close to Tivoli and major attractions. They are in the middle of a massive expansion programme so there was some serious construction activity but it didn't disturb us (we are earlyish risers though think the hammering would have started maybe 8am). The hotel itself is an add on to the pool complex and reception area feels like an afterthought, best thing about the hotel though in a country where they just LOVE to smoke EVERYWHERE, its a non smoking hotel so you can breathe easy. The room was pretty small (which again I think is probably normal by Danish standards, but bright and modern. There was no bar fridge or safe in the room, but there was a vending machine downstairs which had Carlsberg beer in it (yay!) and an ice dispenser. Overall the staff were polite(ish) but not particularly friendly, and the hotel was clean and convenient. We paid about GBP 80 per night for B&B the breakfast was a nice continental smorgasbord.

We stayed here for 2 nights at the end of August. The location is excellent for seeing the sites of Copenhagen. With the train station, Tivoli, town centre, etc all near by it's perfect.

The hotel itself is average for a 3-star. The rooms are large compared to most, but as per other reviews, rather barren and dorm like. Breakfast is outside the hotel at a restaurant that is being attached, but it's not a problem to walk a few steps to and the food was great. The leisure facilities are beyond any I've seen before at a hotel of this class, with the only issue being the early closing time on Friday night.

If I were to recommend one thing from this hotel (and for Copenhagen for that matter), get your hands on a bike. My girlfriend had read about the free city bikes offered by the city. We had planned to use these (you find a bike, put in a 20 DKK piece, take the bike and when you're done, find another lock and get your 20 DKK back), but on our first day we didn't see any anywhere or anyone even riding one. We found out the DGI-byen rented them for about 100 DKK a day, plus a deposit. This was the best decision we made as our 2nd day was a breeze on the bikes.