We are taking a week to spend around the Cote d'Azur - 2 nights in St Tropez, 2 nights in Nice then 2 nights in Monte Carlo. We've booked all but the hotel in Monte Carlo - just not sure where to book? We had a look at the Columbus Hotel, but it seems a bit far from where all the action is, around the port. Is it necessary to have a pool? Or is there a public pool and a decent beach to stay at a hotel with no pool? Or do you have a recommendation as to where we should stay, if our budget is approx 200-250€ per night?