I think the area around Covent Garden / The Strand is a great location. www.strandpalacehotel.co.uk/ has good reviews and I've seen a tourist vlog (video log) from there, and they really liked it.
To travel from St. Pancras, its the Northern Line (black line) 6 stops from King's Cross/St. Pancras to Charring Cross, and a short walk (or black cab) along The Strand to the hotel. On the way back to Heathrow, you are a few minutes from Covent Garden on the Piccadilly Line (dark blue line) straight to Heathrow.
The Strand / Covent Garden area is pretty much bang in the middle between London Eye, Tower Bridge, Westminster Abbey, Harrods's, etc. Tower Bridge and Harrods are about 4 miles away from each other. Within a 2 mile radius of The Strand, you have pretty much most of the main tourist hotspots, all walkable.
You have an endless selection of places to eat, all cuisines at all price ranges. Not sure you'll find anything 'quiet' in that area, unless your going to pay top money for high end places with limited 'covers'.
London is a big mix of everything these days, not sure that what I imagine people think London is, is what it is. But for us locals, for me anyway, London IS a street with an Indian restaurant, next to an Italian restaurant, next to a 'chippie' (Fish and Chip place) next to a French Café, next to a burger place, next to a Moroccan, and a Sushi Bar, and a pub, etc. Covent Garden, Borough Market, Notting Hill feel a bit more London I guess, in a kind of 'Disney/Tourist' way.
It's the mix of people that make this city great, people live and work here from all over the world, and we have 16 million tourists a year, all of which contribute to what London is, and how it feels. I've seen many, many tourist video's where people said they felt 'at home' in London, but couldn't explain why, since they had never been before. The reason is, I think, that they are probably standing within 500 meters of 100 or more of their fellow countrymen, and they are likely to find something familiar from home around every corner.
I get where Jennifer is coming from with Harrods vs. Selfridges, but I would go to Harrods for the 'experience', not necessarily for the shopping. I personally prefer Selfridges if I need to buy something 'posh' but it's hardly typical shopping for Londoners. Strangely, I find Harrods cheaper than Selfridges, especially for food.
Kensington is nice, upmarket and expensive. Paddington isn't bad, a much more affordable area. Shoreditch is young, hip and trendy, maybe not what you are looking for, but worth a visit.