Areas to stay in London

Look into bayswater area. It is walking distance to lotsa sights thru Kensington park, also.
But Tube, grocery, laundry and ethnic restaurants are close by.
You may also ck out Vancouver studios , they have rooms and apts with kitchens in baywater.

"and we may need to be farther out to get what we want for the price we're looking for (around 850-1000 pounds for the week)."

Staying "further out" may be a false economy when you take into account the extra traveling costs and also the time taken to get to attractions.

Agree with both posters. Vancouver Studio Apartments are excellent whether you stay in the main building at Prince's Square or in one of their newer properties near Portabello Road. Have stayed there 3 times. Never displeased. Check out Trip Advisor reviews. I thoroughly enjoy the vibrant Bayswater neighborhood. Easy bus routes along Bayswater and Westbourne roads, two tube stops to choose from (Queensway and Bayswater), nice walk into Kensington Gardens and Hyde Park, same with Portabello Market. Perfect pour at the Royal Exchange pub, stellar and expensive meal at the incredible Beach Blanket Babylon restaurant, a mall, grocers, etc. 20 minute walk or short cab ride from Paddington Station. I also see they now have apartments a bit farther from the main building. Might peruse and see if they match your criteria for a place to stay. Earl's Court is another area to consider. Frommers does a nice concise job of describing London's neighborhoods. http://tinyurl.com/meote8n

The area around Victoria Station is nice and well located. Begravia, Pimlico are the neighborhoods - I have stayed in that area on three occasions, and it always worked out really well.

Bill,

London is easy to get around using the tube.

take a look at booking.com. there are many other search engines too, but it has a map function so you can see where the properties are located and you can filter out the properties and facilities.

just an for your info, all i have found with regards to "grocery stores" are "mom and pop" and Marks & Spence (M&S). Not the biggest but like convenience unless you find a bigger M&S store.

good luck and happy trail.

I also recommend Vancouver Studios in Bayswater.

In addition to the neighborhood, also consider public transportation. I assume you'll use the Tube and buses to get around. Be aware that the Tube regularly closes stations and sometimes entire lines for "planned engineering" (construction), particularly on the weekends. Another plus of VS in Bayswater is that it's close to 3 Tube lines: the District and Circle lines, and the Central line. If one or more lines are closed, you can easily take another or a bus. While you're in London, check the Transport for London website every morning before you leave so you can plan your route: http://www.tfl.gov.uk/tube-dlr-overground/status/. This link shows the status of Underground and DLR (Docklands Light Rail) lines.

If you must have a large " grocery store" experience in London, the Whole Foods market in SoHo should meet your needs.

Whole Food Market is pretty pricey. One of the largest supermarkets in central London is the Waitrose branch in the basement of the John Lewis department store at Oxford Circus.