The trouble with briefcases or anything similar is that you tie up one hand carrying it, and there is the possibility of leaving it behind somewhere accidentally (something you really don't want to do if it includes a concealed gun). So that leaves you with a few options: stuff your pockets, use a backpack, use a fanny pack, or use a murse.
Stuffed pockets are uncomfortable and make it a pain to get what you need when you need it. Backpacks are vulnerable to pick pockets since you can't your eye on things behind your back. And fanny packs, are, well..... just so 1980's and silly looking.
Many years ago I bought what you could call a murse from Coronado Leather and it was/is called a cross carry bag. It is a high quality smallish leather bag with an angled strap so that you carry it over your shoulder and across your body comfortably. This means you have both hands free and the bag is secure and can't be yanked off your shoulder. It is designed to carry what you need, and has a rear compartment specifically designed for carrying a handgun. When traveling on vacation or maybe just going out for the day I sometimes take this "murse" to hold my keys, sunglasses in a case, smartphone, maybe my wallet, and of course my concealed carry gun. Especially in the summer when I am wearing lightweight shorts and a light cotton shirt, where I don't want the weight of filled pockets this cross carry bag comes in mighty handy. Drawing my concealed gun is as easy, or easier than when I am using an IWB or OWB holster on my belt and an untucked shirt. Its about the same ease of draw as using a pocket pistol where you don't have to clear the bottom of your shirt to get to the pocket.
This murse that I own has to be over 10 years old and the high quality, thick leather looks as good as the day I got it. Also, the rear compartment, where the gun goes, has a lock on the zipper. Not much to stop a determined thief if you left the bag unattended, but enough to stop curious grandkids who might find the bag on the bedside table while you are sleeping, giving more security than just having a holstered gun lying out in the open.
If I recall, the cost of this bag was $145, but that was over 10 years ago. I always have my gun holstered as well, inside the bag, so that if I choose to tuck the gun into my belt as an IWB or put it into my pocket I still have that option using my Remora holster.