London Hotel and other questions

Nowhere is going to put you within walking distance of everywhere you're likely to want to visit; Bloomsbury is central enough with good transport links and plenty of places to eat and drink of an evening, but others will have their own favourites.

City Airport is small and business-oriented; it is indeed much calmer to use than London's major international hub airports and has a shorter required check-in time. But don't rule out the train: it's pretty time-efficient to get to Edinburgh (city centre to city centre), and you get to see some scenery en route (and if you stay in Bloomsbury, you're quite close to the relevant station at Kings Cross).

The point of issuing timed tickets is to limit the numbers of people at any one time, and to spread any congestion, so there shouldn't be impossible crowds at any time. You wouldn't be allowed in before your allocated 15-minute slot, certainly, and I would check whatever the Palace website says about it, in case they do insist that you won't be let in to a later slot. As for which time slots are more or less likely to be fully subscribed, who knows?

London is a large city and there is nowhere near all of these places. That said - a central hotel - Maypair, Picadilly, Covent Garden etc - will put you in the center - although you will still want to use the tube to a lot of places. (If you head for South Kensington or similar you are near a few places but too far west for many major sights).

Without knowing a budget and what type of room you want (many rooms are small doubles - one double bed for a couple) - so to be more comfortable you might want a deluxe room or a suite. And without a budget in $ or pounds it's impossible to make recos. Assuming there are ust 2 of you - you might consider looking at 5* places in Central London - as long as you can live with any of the hotels listed.

Frankly I would train to Edinburgh - given the travel time to airports and the often long waits for security et al.

As far as I know the timed tickets to Buck house are limited to those specific times (with perhaps a minute to two in each direction).

The Holiday Inn- Bloomsbury is in central London and might be perfect for you. Its a full service hotel and very nice.My son went to grad school at UCL last year and we always stayed there for price,convenience and location.(I work as a flight attendant and we stay in another part of town that is not so convenient.)
If you are flying into LHR, you need only take the Piccadilly Line at the airport for cheap travel(use an Oyster card for discounted travel) and be at Russell Square tube station in less than 45 minutes with no changes. You literally walk a half block from the tube station and there is the hotel in a real neighborhood. It is across from the Brunswick mall which is perfect for Boots,Waitrose grocery,ATM's,etc. The area is great for cute pubs and restaurants;a few blocks from UCL college,British Museum and British Library and just a few stops on the tube line to Covent Garden and other tourist sites such as Westminster.It is also within walking distance or one tube stop up to Kings Cross station/St. Pancreas where you can take the train to Edinburgh.
If you are going anytime during the Olympics be prepared to have to buy a whole weeks stay during that time at any hotel.

I like the areas around Trafalgar Square, Covent Garden, and Piccadilly Square because many tourist attractions are within walking distance or a short tube ride away. These areas are very busy and crowded, which I prefer, but many people don't want to stay in such hustle-bustle areas. Bloomsbury and Westminster are also good locations.

I second the recommendation to take the train to Edinburgh. I found it easy and convenient, IMO more so than flying.

The only 5-star hotel I have ever stayed at in London is the Royal Horseguards. It is a beautiful hotel overlooking the Thames, across from the London Eye. Marriott County Hall is on the Southbank, also overlooking the Thames right by the London Eye. However, there are many 4-and 5-star hotels in London, and if you state your budget and preference (large chain hotel, boutique hotel, etc), I'm sure you will get several recommendations. You can check pictures on tripadvisor.com to see if a hotel looks too "stuffy and formal". Other good sites for hotels are londontown.com, booking.com, and wotif.com.

Royal Horseguards: http://goo.gl/Xh7vA
Marriott County Hall: http://goo.gl/H6WgB
Strand Palace: http://goo.gl/WSuWn

ETA: Piccadilly Circus, not Piccadilly Square

www.londontown.com/LondonHotel/HOT/Dolphin_House
My fav but many options have gotten some really
good deals bidding priceline.com last Tower hotel
Thames view room older but great views value bid win $80 for me last.Castle View Guest House Edinburgh good for me last good location price views booked on londontown.com

eurocheapo.com great city guide budget hotels for each city.

Have fun!