It's a matter of personal preference, really.
I stay over in Copenhagen about once a month, and tend to go for one of the Andersen Hotel, the Scandic Front or the Wakeup Borgergade - I tend to vary it just because I like change
All have their pluses and minuses. I know the Scandic Webers pretty well, too - it's well located, and a nicely done, old-style Copenhagen hotel. It's on Vesterbrogade, which is a little removed from the full-on red-light district effect of Istedgade, but there are strip clubs a couple of doors down. The Andersen is pretty full-on in terms of surroundings - there's a sex shop over the road, and prostitutes regularly on the corner opposite. There's a hostel down the road too. But I've never (are a fairly tall male) found the area threatening - you just keep aware of your surroundings and take it as it is. I'd say the Andersen is probably my favourite hotel in my budget range at the moment, though - it's been very well renovated, and they're always a friendly bunch. Tripadvisor seems to agree, though, so it's getting more and more booked up!
I personally don't like the area around Tivoli and that end of the Stroget, but I do like the old Kodbyen (meat-packing district) around Halmtorvet in the evening. There's some great places to go on Vesterbrogade itself (including the original Madklubben). Plus, I like to take a bike, ride over to Fisketorvet, over the Cykelslangen bridge and either down Islands Brygge to Christianshavn, or the other way through the woods. It's a wonderful city for cycling around.
Borgergade is a more commercial district, and you're near Nyhavn. It's quieter, and partly residential, but again, has lots of nice eating choices, both in the surrounding street, and up towards Norrebro and the lakes.
I prefer being in the city rather than out at Orestad personally, but the Crowne Plaza beats most of the city centre hotels on value hands down, and the metro is an undeniably easy way to get around. Orestad is both on the metro (to/from the city centre) and the Oresund train line (to/from the airport and Malmo too). It's also easy to get from Orestad down to Dragor, a small but pretty little seaside town "behind" the airport, but surprising tranquil despite this.