I've been to Amsterdam a number of times as well and used to find the hotels in the centre pretty good value. After COVID though the prices seemed to rocket so I started looking a little further out of the city with nearby transport links to get to the centre swiftly.
One hotel I've stayed in that ticked that box was the nhow Amsterdam RAI. Hotels of a similar quality were double the price in the centre. Depends on your budget I suppose.
In terms of Paris, before I first visited I also questioned which arrondissement to stay in and where to stay.
I chose the 5th arrondissement otherwise known as the Latin Quarter and thoroughly enjoyed it. The hotel I stayed in (twice now) was the Hôtel des Grands Hommes.
Just on a side note, Amsterdam is really nice and I personally prefer it to Paris, however it's chocka with tourists these days.
Last year I decided to try somewhere else and went to Utrecht instead which is known as the mini Amsterdam and is just a 30 train ride from Schiphol.
It was indeed smaller but it wasn't packed out, had none of the tat but was just as enjoyable.
Hotel wise I stayed at The Nox Hotel Utrecht which again was fantastic.
Enjoy wherever you go.
