One tip that comes into my mind is that all state-owned museums ( a lot of those) are free on the first sunday of each month. As always with anything free, most museums will have lots of locals visiting. So, I suggest you get up early and get there as soon as they open.

If you´re into Japanese food try any of the restaurants on rue Monsieur le Prince. It runs between Place de l´Odeon and Jardin de Luxembourg RER-station. The places are really cheap. They are that because they have a huge number of guest coming in and out all day. They serve your food fast, thus saving time to do something else.