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it's a really nice town - even if many people do not like it. some people have safety issues, but I never felt anything while stay in the city center. I'd avoid dark places at night though. just be careful.
as for tourism, weather can be quite chilly but don't expect any snow. there are some interesting sights in Marseille - and why not do a day-trip to Aix en Provence?
In my opinion, we don't devote nearly enough scientific research to finding a cure for jerks.
I you have the possibility to change your STAYINGlocation ...I would recommend it... as the train station area is not the safest in town(there is however a good Ibis in the sation premisses) and try to book a room @the Novotel Marseille Vieux Port,or the Residence or the Mercure Bauveau on the Vieux Port.
Yous hould expect a sunny day even if the cold mistral wind is blowing.
As for the sightseeing;
-go for a unique view and a visit of the Bonne Mere Cathedral is a must.
-hicking along the Vieux Port, the PHARO palace park ,the Catalans beach and the Corniche up to... the Pointe Rouge resort;a good opportunity to picnic on the beachside or have a lunch ,the best way to catch the vibrant way of life of marseille.
-visit the old town of Panier and an exhibition at the Vielle Charite Museum.
-a day trip to Aix en Provence and/or Avignon is a must.
-...a visit of Cassis ,the upscale hidden gem,and of course a wine tasting of the rare cassis white wine at the Bar de la Marine
-a mini cruise to Chateau d' If island and ...rediscover Duma's Count of Montecristo... and finally have a drink at the Sofitel's bar
Some good suggestions in there (BTW, the 'Bonne Mère' cathedral is a colloquial/local name for the cathedral officially known as Notre Dame de la Garde). The musée Cantini, while not a rival for any major international museum, has a few interesting things. If you have an interest in architecture, you may also want to have a look at Le Corbusier's 'cité radieuse' on Boulevard Michelet.
To a large extent, weather will condition what you may want to do. Even if it is a bit chilly, if you are lucky to have a few sunny days, taking a drive along the city coastline all the way to the Madrague de Montredon can be very pleasant. Having a bite to eat on the port at Cassis on a calm, sunny winter day is my idea of a civilised lifestyle. On a rainy day (thankfully there are not that many), Marseille itself can look pretty miserable for a tourist, imho.
I would not say that a visit to Aix or Avignon is necessarily a 'must' but certainly Aix is very close and easy to get to so definitely worth considering. Aix is much more tourist-friendly than Marseille: Marseille has a rough-and-ready side to it whereas Aix is more genteel, more 'bourgeois' and reassuring to tourists. It is also more compact and with a higher density of restaurants and cafés.
If you like walking and the weather is nice, you may want to consider a walk in the Calanques (that is the coast between Cassis and Marseille. A calanque is a kind of steep inlet from the sea - not entirely unlike a fjord), either from the Cassis side (easier) or the Marseille one (of if you are fit, do the whole thing and take a train back from Cassis to Marseille). Some of the views are stunning.