I recently stayed for five nights on points at the Marriott London County Hall, having done so once before last fall. I cannot say enough about how well I was treated and most of all the spectacular upgrade to a suite. One of my windows overlooked the BA Eye, the other the Thames and Parliament. The rooms had two televisions and all the modern Marriott bedding. I ate twice at the restaurant and the staff was extraordinarily helpful and the food very good (though the menu is somewhat limited). I was also given two complimentary gifts on arrival.
If there is any downside, it is the Executive Lounge. It is minimalist. There are fruits, croissants, juices and coffee/tea for breakfast, but little else. In the evening they offer wine and beer for a price. There is a computer but the printer doesn't work (as far as I could tell from my talks with others, it hadn't during anyone's experience) and you have to go to the business center to print boarding passes, etc.
Beyond the great suite, the location is phenomenal. You can easily do the South Bank walk all the way to Tower Bridge (I wouldn't suggest the same on the Westminster side unless you walk a lot -- I did it once), passing various book markets, the Tate Modern, Southwark Cathedral along with a lot of nice pubs and restaurants.
Unless you are loaded down with luggage, don't take a taxi from Heathrow. It cost a little more than 2 pounds coming in on the line, with a change to the Jubilee Line at Green Park to Westminster. Although crossing Westminster Bridge to the County Hall can be a hassle because of so many tourists, it is not a long walk. The Heathrow express is another option. For various reasons, I took a cab coming home and it cost 66 pounds without including the tip.
Also, there's a lovely pub between Parliament and Trafalgar Square - the Red Lion - which I highly recommend.