>>Westminster - on Westminster Bridge Road across the street from the Lambeth North Tube Station<<

This isn't Westminster, it's Lambeth. A fairly humdrum sort of area.

>>Liverpool Street - on Folgate Street at the intersection with Shoreditch High Street<<

Well placed for Spitalfields Market and Brick Lane, and for access to the alternative/arty/utterly up themselves bits of Shoreditch/Hoxton. A bit away from the areas most tourists plan to visit (which are west of the centre). I'd be a bit worried about possible traffic noise from Shoreditch High St, a main road, and a but scruffy as a result.

>>Paddington - on Praed near the intersection with Wharf Road; across the street from Edgeware Road Tube Station<<

Although this is on the western side of the centre, again it's not on the doorstep for places you might want to visit.

>>King's Cross - on Gray's Inn Road at Britannia; about 250 meters south of King's Cross Station<<

Again, on a busy traffic road in a fairly humdrum, if gentrifying area.

Looks like a theme: they're cheaper because they're in areas which don't superficially appeal all that much. You've got excellent transport links, but you're getting a discount because the surrounding areas are lacking charm.

A lot depends on where you're likely to want to spend most of your time. From any of these, you're unlikely to be spending more than 20 minutes or so getting to and from most of the places tourists want to go, but you might want to put in some homework at www.tfl.gov.uk to see what sort of travelling you might have to do to get where you want. Start with
http://www.tfl.gov.uk/gettingaround/15101.aspx

Patrick gives a good summary of the various areas - they may not have the cachet or affluence of more popular areas but what they do have in favour is their price. Obviously that's important for you and £50 a night for a double is a bargain in London.

All are near bus/tube stops to take you where you want to go, and you'll want to get familiar with those - Patrick gave you a couple of links.

Westminster/Lambeth is arguably the most central - only a short, but hardly picturesque, walk to the South Bank.

For me, I'd decide on how to you are arriving into/departing from London - so if it's Heathrow, Paddington would have the edge - but only just.

Folgate Street in Spitalfields is a really interesting area on the edge of the City. CHeck out http://www.dennissevershouse.co.uk/ if you stay there.

Even Kings Cross is up and coming these days.

At £50 night and an Oyster card, the world (or London) is your, err.. oyster.

Wouldn't make a decision based on how you're getting to London - if that were the best approach, London wouldn't have hotels anywhere other than near Paddington or Victoria.

Thinking that the King's Cross or Lambeth (that is definitely NOT Westminster - not even close) area places are best. From King's Cross location, you could walk to the British Library and British Museum with ease and won't be too far from Leicester Square.

Liverpool Street Station area is a bit far afield from the tourist attractions, nightlife and shows. Paddington area isn't that great for tourists either.

Make sure the reviews are, at least, not terrible. London hotels that cheap are usually so for a reason.

Oh there's nightlife around Liverpool St and Shoreditch/Hoxton - certainly more than Lambeth (which is a mixed residential and small business area) - if you're of the appropriate age and cultural disposition.

So much depends on the OP's own tastes and interests: s/he might get a good idea of whether any of these areas would fit from a guidebook or two and/or http://www.timeout.com/london/

<<Wouldn't make a decision based on how you're getting to London - if that were the best approach, London wouldn't have hotels anywhere other than near Paddington or Victoria.>>

All things being equal; the hotels are in similar locations (slightly out of the way but perfectly OK), and they are very equal, then choosing a hotel on how the OP is arriving makes perfect sense.

If travelling from the north I wouldn't necessarily head south of the river. If coming from the south, then heading to Lambeth rather than Kings Cross may make more sense. And if coming from the west why trek all the way east? These distinctions come into play when there's little to choose between the areas.

There are hotels all over London catering for travellers who arrive from all points of the compass,

Thinking Lambeth's proximity to South Bank as to nightlife perspective, but PL is local . . . .

I think I have narrowed it down to either Paddington or King's Cross, which is based upon transportation. When no location came out as the crowd favorite, I looked at the origin stations for my day trips and my next stop, which is Bath. Two of my trips depart from Paddington and two from King's Cross/St. Pancras. The final day trip departs from London Bridge, which is convenient to none of the options.

By the way, BigRuss, I happened upon these hotels because of the rave reviews. All the locations have four or four and a half stars with hundreds of reviews on TripAdvisor.

Paddington would be my LAST choice of the four. Kings Cross maybe would win out by a nose over the other two -- but definitely not Paddington IMO.