More details needed.
Define 'reasonable'
By Buckingham, do you mean 'Changing of the Guard'?

Any central London location will do, since you will need to take the Tube to see these sites. I like Bloomsbury area, which is on Tube line for Heathrow. From there I walked to st Paul's, Covent garden, Trafalgar Sq,etc.. From Trafalgar, you could do Big Ben and Buckingham.

You could easily see this in your time. Tower of London should be done first thing in the morning. I would ski the changing of the guards, takes too long and you don't see that much.

We just want to walk by Buckingham palace. i'd love to go inside, but from what I hear the tours are not really worth it. Your input?

I would say something that is not a one star but nothing as fancy/expensive as a four or five star. We want to be able to sleep comfortably and not in area that is noisy at night since we are light sleepers.

London is expensive. People here use Priceline to lower those costs.

Budget?

Another option is B&Bs. There are several in the Bloomsbury area.

OK. yes, the walk from Trafalgar Sq. to Buckingham is nice. Have a look at London Walks, they have tours that cover the area.

Perhaps one day Tower & St Paul's. Other day and 1/2: Covent Garden, Trafalgar,etc..

WHAT IS YOUR PRICE RANGE? The star categories say nothing -- UK star ratings are primarily based upon amenities offered by the hotel. Your description of what you are looking for contains no useful information. London hotel prices are analogous to Chicago or New York costs.

What is "convenient"? If you mean walking distance, that hotel really doesn't exist. London is the largest and most populous city in Western Europe, it is not small and confined. If by convenient you mean close to easy transportation to where you want to go, most (if not all) of central London would qualify.

"We just want to walk by Buckingham palace. i'd love to go inside, but from what I hear the tours are not really worth it. Your input?"

The tours are VERY worth it. However they are only offered from late July to the beginning of October, so when are you going?

You say >>such as the Lime Tree Hotel<< - so what is wrong w/ the Lime Tree? It is in a very convenient location near Victoria Station

Oh - meant to ask -- You say 2.5 days -- are you counting your arrival day as a full day or a 1/2 day? Because arriving at 09:30 doesn't net you a full day in London. You won't get to your hotel until at least noon but more likely a bit later.

So after checking in you will have about 1/2 a day on day 1.

Except for the above mentioned tour period, Buckingham Palace is just a walk-by, as is Big Ben. So you have only mentioned two sites that take time -- 3-4 hours at the Tower, and 90mins to 2 hours at St Paul's.

If you arrive at the Tower at opening time on day 2, stay until just after lunch, then over to St Pauls -- that is a good use of time and leaves the rest of your days free to see whatever you want.

You will find loads of budget hotels and B&B's in central london and depending on the month you are visiting you could get it at a bargain or end up spending quite a premium.

Try and base yourself around the Picaddily line for easy and cost efficient transfers to the airport, so you can begin by searching for places close to the tube stations - these are likely to be more expensive than say a place which is two streets away.

If you intention is to see only the places you have listed you should be ok. Tower of London is probably going to take up your maximum time amongst the places listed.

We arrive the morning of the 30th March. Lime tree is booked thus why we can't use it. Is there a website I can go to search for hotels/b&b's in central london? I assume Piccadilly circus will be a good location?
price range would be $100-150 a night.

"I assume Piccadilly circus will be a good location? "

Not really -- it is very congested and not that many hotels. Jellys_wundermum mentioned the Piccadilly tube line -- not Piccadilly Circus specifically.

Good areas along the Pic. line would include South Kensington, (some budget accommodations in the area), Knightsbridge/Green Park (almost NO budget accommodations), Holborn/Russell Square (some budget places).

There are many budget places near Victoria and it would be convenient too. It isn't on the Piccadilly tune line - but it is easy to get to w/ one change of lines at Hammersmith, and is on the direct tube lines to the Tower of London and Big Ben.

Londontown.com is a good site with hotels in all price ranges. Your $100-$150 = approx £60-£95-ish

As a P.S. Holborn/Russell Sq. would be Bloomsbury.

As a sample B&B:

www.harlingfordhotel.com

It is a rather upscale B&B. Note that the word 'hotel' in London does not necessarily mean hotel, could also be a B&B

Does the Picadilly line go all the way from the airport to Russel Square stop? If so are there lifts from the platforms or only steps ( thinking of carting our luggage )?

Yes -- the piccadilly line connects LHR w/ all those areas mentioned above inc. Russell Sq. Most London tube stations have at least some steps. Russell Sq uses elevators.

If you are carrying reasonably sized luggage you should be able to manage. But even the step-free stations have some long walks (and there are long walks at LHR too). So if you'll have a hard time w/ the bags, you can pre-book a car service. It costs more but is door-to-door and there is no luggage schlepping

Thanks janisj.

Piccadilly would NOT be a quiet area. South Kensington is quiet, Russell Square not too bad. I'm eyeing Kensington High Street/Holland Park for our next visit, but don't know how many inexpensive hotels are around there. It does depend if the hotel is on a busy street, but you can always ask for a quiet room -- and check it out when you arrive.

I found a decent hotel located at heart of Earls Court (in the Royal Borough of Kensington & Chelsea). Is this a conveniently located hotel? The price they are giving me is $114 a night.

Earl's Court is convenient to a Tube ride that will take a while to get to central London. It is not convenient (walking distance or even bus ride distance) to any major attractions, and certainly none of the ones you mentioned in your initial post.

And it's also not close to any main rail station other than Paddington, which may or may not be an issue for any proposed day trips.

Thank you BigRuss. This was one in which I searched for that fell in the South Kensington area. It is getting harder than I thought to book this hotel!

ok, I found a place located in Belgravia, is this a good location?

Yes, Belgravis is a very good location, very central. Jump on it!