Your tips I would recommend staying in a quiet neighborhood such as Kensington, Chelsea, etc. Transportation is easy on the tube. You will get a good night's sleep and be ready for the next day of activity in the West End and other busier areas. Go to Canary Wharf to experience fantastic shopping.
London is thriving and there is so much to do including seeing plays, opera, visiting museums and palaces as well as experiencing great restaurants and shopping. The tube was a bit crowded, especially on the Piccadilly line, but other than that, public transportation is a breeze. The Oyster Card is a must if you are staying for 5+ days.