One of the great things about commuting, or running errands, on a bicycle is that you can do those things while outdoors (sorry, driving a car is on the “in” side of the doors)!
The downside of cycling is that carrying all your stuff with you can be problematic, particularly in light of the fact that when you stop you must take it all with you.
Panniers, saddle bags, and handle bar bags are by far the best way to carry stuff. If, however, you are getting on and off almost as much as you are riding, the dismounting and remounting of these bags becomes quite tedious, and everywhere you go you look like a cyclist who just ran away from home.
Putting your stuff in a day pack and wearing it solves these problems. It automatically comes with you when you dismount, and everywhere you go you look like everyone else with a day pack.
While a pack will never match the efficiency and comfort of panniers, you can mitigate the packs shortcomings in two ways - keep the weight low, and get a superb pack.
First, mount your lock on the frame, this will save weight, and you will not be taking your lock with you anyway. Second, do not get a large pack, too much capacity encourages too much weight. Consider an upper limit of around 1800 cubic inches (30 liters).
My favorite pack for this application is the Osprey Talon 22 (22 liters or 1350 cubic inches). It is quite light in its own right, and unless you fill it with bricks its capacity will keep you within a reasonable weight range. Innovative features include a bladder sleeve outside the main body of the pack, and an outside pouch for overflow or quick access.
Bike-specific features include a tab for a tail light, and a retainer for fixing the helmet to the pack - this is a delight when you really want the helmet out of the way.
The pack comes in two sizes, both of which are widely adjustable. It is constructed in such a way as to support the load while remaining flexible enough to move with your body. Compression straps stabilize the load when the pack is not filled to capacity.
All these features make the Talon 22 a superb pack for the bike. They also make the pack superb on the trail. This double-duty feature may be the best of all.