Having stayed at both the Chancery Court and the County Hall, I would just take issue with 3 of John69's laments:
1). No hotel in London, or for that matter Europe, is prepared to weather a heat wave like Europe recently experienced. Their air conditioning simply is not designed to American standards vis a vis BTU's, etc., so if there is a heat wave, invariably wherever you stay most probably will come up short.
2). Others have mentioned another bridge that one may take across the Thames to the County Hall from the other bank near the Embankment Tube stop, and I personally have walked the 5-10 minutes necessary to get to London Waterloo staion and tube stop (where the Eurostar arrive from the Continent) and it is not bad at all.
3). Moreover, if one were to walk that way, one would discover a number of small eateries behind the County Hall -- at least 4 - 5 -- and they range from a Yo Sushi conveuor belt restaurant, to a Turkish-Mediterrranean resto, to an excellent Fish Restaurant known appropriately as "Fish", to a take-away/takeout noodle place, to a pub.
That hardly amounts to just McDonalds, and having eaten the food from the noodle place -- which delivers -- and at the Fish Resto, I must heartily disagree.
Although I agree that at the Chancery you probably will get more bang for your $$/MR points, if you are a first time visitor to London, then I would not suggest the Chancery, and instead suggest the County Hall or either the Park Lane or the Grovesnor, both of the latter are in the tony and posh area of Mayfair -- as well as perhaps considering the 47th ST Park property.
Finally, the Saatchi Gallery has just moved to the County Hall, and what with the London Eye next door to the County Hall, the Tate Modern and the Globe downstream, and the Houses of Parlliament and Big Ben across the Thames, this is a great introduction to London, for those who are not so jaded, or who are otherwise there on business.