This is the bus company that provides at least some of the bus service out of Aix: https://www.lepilote.com/fr/itineraires/4/JourneyPlanner/Index
In my experience the staff at local tourist offices are pleased to make suggestions for side-trips to visitors who have enough time in the area to go to some of the less well-known destinations. Explain that you'll be taking buses or trains and ask what would make an interesting day. They may even be able to give you a print-out of the train or bus schedule.
Cassis is a viable day-trip from Aix. Travel time will be close to 2 hours each way--a longer trip than I'd usually want to make. However, Cassis is fairly small and you don't need 12 hours to see it, and you have a lot of time in Aix, so you're probably going to end up needing to take some longer day-trips. For Cassis it appears you have a choice between two buses (changing at Pole d'Exchanges, whatever/wherever that is) and a train/bus combo (changing in Marseille). I would certainly try to take different routes out and back for a change of scenery. In addition to walking around the town of Cassis, you can take a boat trip (weather permitting, I suppose) to the Calanques. There are also trips to the Calanques from the harbor in Marseille. I got this transportation info from Rome2Rio, but you must be super cautious about using that web site. I've found it to be unreliable as to travel times, frequencies and fares. What it's good for is telling you whether public transportation is available at all, where you'll probably need to transfer and what company runs the buses. Just keep drilling down for that information, then go to the bus-company website for specifics. For train service check the SNCF website.
For someone who enjoys walking a lot (as I do) there would be enough to see in Marseille to justify more than one trip there. I enjoyed seeing Vallon des Auffes, the old fishing harbor, as one example.
An option on the outskirts of Aix itself is Camp des Milles, a WWII internment camp that funneled people to the transit camp at Drancy, from which most were sent to concentration and death camps farther east. It has been turned into a memorial site and museum. Very modern and well-done; it's new enough it may not be mentioned in some guide books. Practically all the psoted information has been translated into English. There's bus service from the the center of town. The lower level of the complex is quite chilly even on hot summer days, so take a wrap of some sort.