There aren't "bad" places near Alkmaar to stay, but we'd recommend being within walking distance to lovely, interesting things. The city center is excellent, and the neighborhoods to the west and south are beautiful (see highlighted areas in the map above).
Yes. "People travelling from within the EU/Schengen area who can show proof of vaccination can travel to the Netherlands." This is according to the Dutch health website as of 23 Mar (link in the Travel Page).
Nope! The proof of vaccination and negative test are sufficient.