Hey I'll be in London over New Years and was wondering if anybody had a comment on which areas of London are safe for a single female to be staying in/around. I want to be close to the sights (walking distance-ish) and not pay heaps for a hotel, but don't want some dodgy drugged up neighbourhood either. Any thoughts on Earl's Court, Kensington, Victoria, Bloomsbury, Marble Arch, Paddington, King's Court...?
And any thoughts on using the tube alone at night?
thanks :)

Out of that list I would feel the safest in Kensington and Marble Arch. Obviously Marble Arch is more central plus it's on the Central Line which is handy for getting to places.
The tube is fine late at night as long as you use common sense and don't dress provocatively i.e miniskirt and tits hanging out and don't get involved in a conversation if somebody approaches you. Just smile sweetly and move away. It's the same in London as it is in any big city, don't wander around poorly lit areas on your own and most of all use your head. Don't have obvious tourist paraphernalia hanging out like cameras & maps. Also if a situation arises on the tube that you really don't like the look of you can always get off and even go upstairs where the staff are and get the next train (provided it's not the last train of course)
Have a good time!

No area is 100% safe. Bear that in mind and you should be OK.
The places you mention are all central tourist areas (Kings Court doesn't exist. If you mena Kings Cross - its a bit seedy and did have a problem, but might be OK now. I don't know).

I stayed alone in Kensington, and loved the area. It was more of a residential neighborhood with a couple of hotels here & there. It was somewhat more upscale -- even though I was staying in a budget hotel, someone in a flat across the street owned a Rolls Royce. A very interesting mix of people.

We stayed in the Pimilico/Belgravia area. It was fine, fairly quiet with a selection of bars/restaurants. It was also possible to walk to most of the attractions (we never used the tube).

As above. All OK except Kings Cross - still seedy #2, drunks and junkies on the some streets. Maybe they will try to clean it up when the new Eurostar terminal opens at St Pancras.

As a rule it's hard to divide London up into 'good' areas and 'bad' areas. There are good bits and bad bits thrown together in a seemingly completely random way.

I have seen what others have posted, and I have to agree, but we lucked out and stayed in a great
(well, it was clean and cheap) place near Kings cross. www.hotelarriva.co.uk/ is run by some find of eastren eruo family who are unfreindly but run a clean budget place that I felt was safe. Well lit streets and if you are consurned, take a taxi the 3 blocks from the tube. worth a look

All the places you list are basically fine except I would definitely avoid King's Cross, and possibly Paddington.
Earls Court has lots of cheap/reasonably priced very decent hotels (£50-75) with good pubs, shopping, and easy tube/bus access to anywhere you want to go.
And the "sights" in London are spread over well more than a hundred square miles. There is NO area in London that is within walking distance of all "the sights." Maybe you should mention what particular "sights" interest you, and then you could get more specific recommendations for appropriate neighborhoods. But virtually every tourist in London who wants to see a lot gets from area to area using public transportation, so staying in a hotel close to a tube stop not too far from the center of London is usually a very good idea, unless your budget won't allow it.