Hi,
I'll deal with these the wrong way round. First you can get info on the EuroStar trains at www.eurostar.com and I have posted what info I have about this in reply to a previous request for Eurostar info in the Europe Forum ( see <a href="http://nonrev.net/eve/forums?a=tpc&s=93260999&f=55260999&m=711103545" target="_blank">http://nonrev.net/eve/forums?a=tpc&s=93260...999&m=711103545</A> ).
In respect of sightseeing in and around London I have also previously posted some general info on this in reply to item
<a href="http://nonrev.net/eve/forums?a=tpc&s=93260999&f=55260999&m=745103776" target="_blank">http://nonrev.net/eve/forums?a=tpc&s=93260...999&m=745103776</A>.
Where to stay in London depends a lot on what you want to see and how long you intend to stay but I would avoid LHR as you will spend 1 1/2-2hrs each day travelling into Central London, although its an OK location if you want to check out Windsor/Eton. In general most areas of London are safe. There are, as with any large city, iffy areas however you'd not normally find tourist accomodation therein.
As you can imagine in a city like London actual accomodation can vary dramatically in both stature and price depending upon your needs. Most of the big hotel chains offer travel agent discounts based on space availability. If you have an idea of what you want let me know and I'll see if I can be of more specific help.
In respect of Paris, public transport and Rover passes are again the most flexible way of getting around but yet again it depends on what you want to see. If you have more detailed ideas then let me know and I'll try to be more specific. See also post <a href="http://nonrev.net/eve/forums?a=tpc&s=93260999&f=55260999&m=711103545" target="_blank">http://nonrev.net/eve/forums?a=tpc&s=93260...999&m=711103545</A>.
I'd also suggest putting a post on the North America forum to ask if anyone there has any specific recommendations for London or Paris Accomodation as personal experience is the best advert.