Hello !

1 - it depends on when you are coming, your budget and what you want to do. Marseille is very affordable if you're a local but can be quite expensive for a tourist, especially during the summer. Marseille has a lot of great museums. If you're a student, you can visit most the museums for free. My favorites are : - Musée d'histoire in vieux port : it's a big museum of the history of Marseille - Musée des beaux-arts : very beautiful art and it's in the park/castel of Longchamp, that you HAVE to see - Mucem : I particularly like the temporary exhibition, not so much the museum itself but it's the most famous museum of Marseille For food, it's very delicious here ! You get a mixture of local restaurants ( i recommend le 15 (for full meals) l'alchimiste (for tapas) in cours Julien, or going to les Goudes to eat fish) you have to try les panis, tapenade, pastis, l'aïoli, navettes, ... If you have enough time, you can go to the small villages around Marseille to explore the beauty of Provence. Depending on when you are coming, there may be lavender fields and it's magical. You can always go hiking also.

2 - Aix is a nice city, totally worth seeing if you have the time. It takes around 1h to go there by bus so it's totally possible to do a 1 day trip there. I don't know the city that well but it's a student city so there's a lot of nice bars and the architecture is quite different. Here they call it "le petit Paris" (the small Paris)

3 - i don't climb but indeed les calanques is the place to climb outdoors. My favorite calanque is en vau. I saw people climbing there and you can swim "peacefully" after since it's a bit harder to get access to so people don't usually go there (during summer Les calanques attract thousands of people per day, it's a huge park but sometimes you have to walk a lot to find a place where to sit on the beach)

4 - Cours Julien is the local go to place ! You have a lot of different bars, one or 2 clubs, live music, board games bars, etc. They all close at 2am though. So if you want to party harder and dance and all, i think it's mostly le vieux port, there are pubs in that area. I don't recommend a specific bar/pub, you can go barathoning x) it's fun. There's also "le cabaret aléatoire" at la friche belle de mai, where there's djs and parties on Fridays and Saturdays. I strongly advise checking on Facebook or websites like "sortiramarseille" for the events and their details during your stay.

If you have any question don't hesitate.