This is certainly a doable plan, and with only one night you can pack light, leaving most of your baggage wherever you're staying in London. Take an early morning Eurostar and you'll have most of the day to explore Paris as you plan. Then get an early train to Vernon the next morning. Giverny might take half a day, getting you back to your hotel (and bag you left there) in time to reach Gare du Nord for your return Eurostar -- making sure to allow plenty of time for check-in, as Chris noted. They have airport-type security, and passport control is at the departure point going both ways.
There are thousands of hotels in all price ranges in Paris. I'd suggest starting with booking.com, plug in some budget and other parameters and see what you find. The closer to the river, the more it will cost, other things being equal. The neighborhood around Gare du Nord isn't the most charming, but would be very convenient for your plan.
This makes so much more sense than a one-day trip from London to Paris and back, which so many people seem to want to do. Obviously your plan only scratches the surface of Paris, but you'll have time to appreciate the city and start thinking about what to do on your next, longer, visit.
BTW if you're a Monet fan you might also want to try for the Musee Marmottan, in the Passy district west of central Paris. The Metro stop is La Muette on line 9.