Kind of depends on your definition of "dress up". Nobody is wearing suits and few wear ties.
Assume you are talking about dinner. Breakfast and lunch - no.
Assuming you are asking as a male - I think the gals can do anything they want
There are two main restaurants (although there is a third on the roof top - Gastro? - but I haven't been there).
Pearl (that's the name of the fancy restaurant at Pearl) is, well, fancy. You have to wear closed toe shoes, long pants. Now that is still a wide range of options. One of the most frequent questions is about whether jeans are "nice enough". Lots of opinions. Mine is "no" - along the lines of "The gals are dressing up so you should make an effort to step it up as well.". Yes, there are nice/expensive jeans - but they are still jeans. Most of the guys will be dressy casual.
The other restaurant - Aphrodite - is a bit more casual but still has a nice ambiance at night for dinner. For me, the dress code is the same for both. Have you ever been some place and felt under dressed? You *might* feel that way if you don't at least go with nice pants and a button down shirt. You *can* wear shorts at Aphrodite (I think) but you might feel like you stand out (and not in the good way from looking at your wife in a club dress).
All that is just my opinion and there are plenty of other, legitimate opinions that differ. I suggest you spend some time reading posts on the forum to get a feel for things.