I stayed 4x at Premier Inn London Waterloo (Westerminster Bridge) (hotel entrance street level). Across a small plaza is Premier Inn London County Hall ( hotel entrance is up a couple of steps). Both hotels have A/C, bar, restaurant, close to London Eye, Westminster Abbey, Thamas river, Big Ben, Parliament, HOHO, regular bus, 2 tube station, Waterloo Train station, pubs, restaurants.
I took Justairports (car service) from hotel to LHR. Have also used them from LHR to hotel. Price is per car, use hotel's postal code to get price.
Depending on your dates, Buckingham Palace's royal staterooms may be open to the public.
www.internationalfriends.co.uk
www.londontoolkit.com
www.justairports.com
www.londoneye.com
www.premierinn.com
www.rct.uk (Royal Collection Trust - Buckingham Palace)
www.westminster-abbey.org (get tickets in advance) (can purchase inside the Abbey ticket for a guided tour - worth the money)
www.theorginaltour.com (HOHO)
www.bigbustours.com (HOHO)