Help with itinerary please

We are going to London from July 25th thru July 31st. Then we want to go somewhere to vacation thats close by from August 1st thru August 8th. We our family of 5 were thinking if starting at London 5-6 nights then taking the Eurostar to Paris with a connecter to Nice, car rental drive to French Riviera staying maybe in Cannes. I’ve to Nice and Monte Carlo before. Okay then taking the train back to paris then from there to Hamburg Germany staying there one week because of Family wedding then raking a train to amsterdam which is the closest to hamburg and flying back home. Total of one month almost. I already booked my flight then started looking for hotels. Come to find out Cannes is so expensive to book a hotel plus we need two rooms. The good hotels cost around 700 dollars a night. (Martinez hotel, JW Marriott). So I was thinking to save money because we have to stay in London, hamburg, amsterdam should I change my itinerary from french riviera to maybe barcelona spain? Which close country would you suggest that won’t be as pricey to stay for 7-8 days? I would love to go to Italy and that would be my first and only choice however its so far away from london, Paris. Also I am worried about all the hassle from one place to another. I would like something easy and convenient to stay a full week and relax. Thank you in advance. I would appreciate all your ideas please.