where is the Eurostar train located in London & where do we land in Paris?

Yvonne,

The EuroStar leaves from London St. Pancras station (which was just completely renovated in the last year or two). Arrival in Paris is at Gare du Nord. The stations in both London and Paris are easily reachable via Tube / Metro.

You might check the Guidebooks for "reasonably priced" Hotel listings. I'm assuming you're going to be in each city for a few days, so I'd probably choose Hotel location based on convenience for touring.

Happy travels!

Not sure about hotels near the stations, and I recall the area around Gare du Nord to be sort of iffy. Plus, it's very far north of central Paris. I can recommend the following:

London Victoria Station area (quiet residential area in central London with easy access to other stations): Cherry Court Hotel or Blades Hotel. Check them out online or in Rick's guidebooks.

Paris 7th arrondissement (central Paris Tour Eiffel area): Hotel de la Tulipe. Other good options in the Rue Cler area are the Hotel Leveque and Hotel du Champ de Mars, but these two book up quickly.

For London, there are loads of small and large hotels located just across the street from St Pancras. If you search on Google for "hotels near st pancras, london" you will find plenty.

Paris is a different story - the area around Gare du Nord can be dodgy at night (although it has vastly improved in the past 3 years). Unless you have a specific reason to stay there, I also second the recommendation to stay somehere else. There are plenty of direct tube lines from Gare du Nord to all areas of the city. One nicer area not far away is Place Republique. If you really want to stay next to Gare du Nord maybe due to your train schedules try to book at the Mercure Terminus Nord.