The Eurostar trains to Eindhoven run on a very regular basis from St Pancras Station in London with a couple of changes required along the route. The first part of the journey to Amsterdam takes between four and a half to five hours on the high speed Thalys or IC trains, changing at Brussels and Rotterdam. Disembark at Amsterdam to take the direct train to Eindhoven; journey duration about 1 hour and twenty minutes. Arrival is at the Eindhoven's Central Station which is conveniently located right in the city centre along with the adjoining bus station. Local train services run from the Central Station and also the nearby smaller Eindhoven Beukenlaan Station. Taxis are available at the various station entrances, where access to the many bus routes around the city can be found.
The city of Eindhoven is located in the southern province of Brabant and is the fifth largest in the Netherlands with easy access to Amsterdam, Rotterdam, D├╝sseldorf and Antwerp. It has grown from a small town in the thirteenth century to a large thriving commercial centre for global companies like Philips. There are fantastic shopping facilities that are open seven days a week in the city centre. World class museums and galleries abound, along with numerous art works displayed in open public places, such as the Flying Pins and Swing sculptors. The city has a buzzing nightlife with a fantastic choice of venues, events and social scenes for all tastes.
Here are some other resources that might have the information you need