You might consider:
Arkel Bug , which works as a backpack.
Quite modern, sporty look.
Ortlieb Downtown , which has a comfortable shoulder strap.
You might check other products of those two producers, if you need a bigger/smaller cargo capacity.
Both of these panniers are very easy to attach to your bike.
Perfect for your daily commuting needs and running errands.
bicycles.stackexchange.com/users/122/Tadeusz A. Kadłubowski
I've tried several options here, including specialty options like Arkel's laptop bag with a shoulder strap.
There are some things that I didn't like about carrying panniers off-bike.
The attachment hardware adds extra weight that I'd prefer not to have.
The hardware always seem to find a way to bump into my side, even when it's covered.
And finally, sometimes I just don't to immediately be identified as a cyclist when I walk into room, based on the bags I'm carrying in.(Orange bags with reflective strips
don't go great with formal attire and settings)
My recommendation is to choose a bag that works for you off-bike, and find a way to carry that bag on your bike.
For example, Clarijs makes some large size panniers that made to reside on the bike.
The would be large enough to drop another bag into: Another option is a front rack.
Workcycles has a giant, masculine box if that's your thing.
It apparently isn't getting stolen while parked on the streets of Amsterdam, so it will likely survive live in your location as well:
Cargo bikes like the XtraCycle, Yuba Mundo and bakfiets also have permanent storage capacity in the form of standard bags or boxes, and this is what I'm used to using frequently myself now.
Here's the giant Go-Getter bag, which as you can see can easily swallow several other bags with in it: Given all the above, my "off-bike pannier" is the Walking Bag by Courierware .
It basically looks like a black shoulder bag.
It's designed as a kind of small courier bag, but it doesn't scream "CYCLIST ACCESSORY" when you walk into a room due the smaller form factor.
It is however basically waterproof and easy to fill and access.
For simple, shorter trips, I can cinch down the strap and where it over my shoulder like a courier bag.
For heavier loads or longer trips, I currently drop it into my XtraCycle bag and go.
bicycles.stackexchange.com/users/2001/Mark Stosberg
I use an Altura pannier (or both if I'm caring a lot and need the full 46 capacity), and a detachable shoulder strap that I keep in the top pocket of the pannier.
It's on the bike most of the time, but when I need to take it off and carry it round the strap is always there handy, and the rixen & kaul fittings make the pannier easy to attach/detach.
It's not quite as comfortable as a dedicated over-the-shoulder-bag (sometimes the pannier clips can get in the way as I'm walking about), but it's definitely good enough for what I need.
bicycles.stackexchange.com/users/96/Wilka
I have an Arkel Bug and an Arkel Briefcase , and I think that they are great.
Both have straps that can be used over the shoulders, in fact, a shoulder bag can be added to any pannier.
I use the Bug for my clothes, lunch, and tools, and the briefcase for my laptop and other work related items.
They are convenient to use easy to carry around, and Arkel makes high quality panniers.
They are pricey, but worth it.
The way that the laptop holder in the briefcase is built provides shock absorption.
It is worth noting that the backpack functionality of the bug is inferior to that of a regular backpack, there is always a metal bar on your back.
Arkel has one of the best attachment systems , it keeps the bags secure even without the bungee cord.
Jandd also makes great panniers and some of the best racks, but I found that their briefcase was poorly made when I tried it out in 2006 (same year I purchased the Arkel bags above).
They have changed the material and possibly the quality since then, so it might be worth checking out.
Another drawback is that it hangs sideways rather than 'right side up'.
bicycles.stackexchange.com/users/839/David LeBauer
I would suggest the Woodward Convertible from North St. Bags .
To be fair, I work for them, but given the nature of your inquiry and the tasks you're looking to achieve, this product is perfect.
We've designed the Woodward to work well both on and off the bike and we have worked hard to make the transition process easy and quick.
bicycles.stackexchange.com/users/26541/Kevin Murphy
Not to confuse anyone, but we at North St. Bags also make a second convertible pannier backpack, the Route 9 .
This bag is designed as more of a long haul touring option with less frequent on and off transition than that of our other bag, the Woodward Convertible .
Depending on the nature and length of your ride, you may prefer one design over the other.
But both are quick converting options that are great sellers for us.
The goal was an uber simple design, using quality Made in USA materials, made in house in Portland, Oregon.
We sell these bags to about 60 bike shops throughout the USA.
Also we have a sizable following in Japan and we do in fact ship worldwide direct to consumer.
bicycles.stackexchange.com/users/26541/Kevin Murphy
I got a North St Bags Woodward Convertible Pannier/Backpack and use it all the time.
It has hidden backpack straps which make it easy to wear on your back and quickly converts to a standard pannier for mounting on your rack.
bicycles.stackexchange.com/users/2997/Benzo
I'm looking for panniers. I mostly just potter around town, and am not planning any cycle touring so my main criteria is that the panniers should be easy to carry around off the bike. Built in rucksack straps or a shoulder/cross-body strap would be good. Just a carry handle would not be enough for me.
Recommendation for panniers used off the bike a lot
bicycles.stackexchange.com
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bicycles.stackexchange.com/questions/762
bicycles.stackexchange.com/users/335/Hamish Downer
Arkel, North St. Bags, Clarijs, Workcycle and Altura make panniers that are also uasable as rucksacks. Another option is to buy a rucksack and then find a way to attach it to the bike. There are also cargo bikes that have permanent storage built-in There is a number of available panniers that can be used off the bike and may be converted into a backpack or a bag with a shoulder strap. These include the Arkel Bug, the Ortlieb Downtown, the Altura pannier, the Arkel Briefcase and the Woodward Convertible aiming others. However, panniers are not necessarily mobile. You could try large panniers with greater storage capacities that are designed to stay on the bike. Cargo bikes often have built-in or fixed storage spaces, while some bikes are equipped with front racks.
There is a number of available panniers that can be used off the bike and may be converted into a backpack or a bag with a shoulder strap. These include the Arkel Bug, the Ortlieb Downtown, the Altura pannier, the Arkel Briefcase and the Woodward Convertible aiming others. Panniers are not necessarily mobile. You could try large panniers with greater storage capacities that are designed to stay on the bike. Cargo bikes often have built-in or fixed storage spaces, while some bikes are equipped with front racks.