Marseille spreads a long way, so the choice is really between the old streets stacked above the Vieux-Port, the going-out slopes behind the Canebière, and the cheaper, rougher ground around the station.
Le Panier — the old quarter above the port
The oldest part of the city, on the slope north of the Vieux-Port: narrow stepped lanes, mostly closed to through traffic, and a walk of a few minutes down to the harbour and the waterfront museums. You trade car access and quiet for being able to leave the hotel and be somewhere worth standing in two minutes.
Vieux-Port and Opéra — walk to everything
The harbour itself and the blocks behind it, where the metro, the boats to the islands and the 50-centime Ferry Boat all leave from. It is the most expensive ground in the city and some streets stay loud until early morning, but nothing else puts you this close to the water.
Cours Julien and Notre-Dame-du-Mont — the going-out slope
A hillside of small squares above the Canebière, painted end to end, with most of the city's bars and small restaurants packed into a few blocks. Good if you want to walk home from dinner; bad if you want to sleep before one in the morning, because the noise is in the street rather than inside the venues.
Practical tip — cheap beds near Gare Saint-Charles
The streets below the station and around Belsunce hold the cheapest rooms in Marseille and put you on both metro lines, which matters because the city is too big to walk end to end. The area is scruffy and feels unwelcoming after dark; if that is a problem, the Joliette side is a similar price, newer and much quieter, though it empties out completely at night.