If you have your heart set on a specific restaurant (particularly one of the city’s nicer places), then reservations are essential during the high season (spring and fall). However, it’s not unheard of to walk in and get a table, particularly midweek.
Although the city is bustling, there are relatively few instances where reservations are necessary. It’s advisable to get tour tickets in advance if you’re looking for something like the "haunted hearse" tours or others with relatively limited seating. Walking tours should also be set up in advance, particularly with the smaller tour companies.