Depends on what you mean by "day bag". On embarkation day, I use my usual carry on bag (it's now a backpack). For port excursions, it will entirely depend on where I'm going and what I'm doing. Since we don't do beaches, it's usually just a cross-body purse. For daytime on board ship, it's usually just my lanyard and phone or iPad depending on what we're doing. If I'm reading, it's my iPad. If we're just walking around, it's my phone if I have a pocket. If I don't have a pocket and I particularly want my phone with me, I have a wristlet that I use for it.