Think about how you're actually shooting when you "walk around". If by "walk around" you mean "walking up a mountain trail and shooting huge vistas and wildlife on the way" then sure, you're going to want a lot of range and you're probably going to want at least two lenses. But if by "walk around" you mean "walking around the middle of a town with my family" then you'd most likely be better off with something like a single, light prime lens.
If you really do think you're in that first camp, the big two lenses to pair up are the 16-35 f/4 IS and 70-200 f/4 IS. They have near-identical rendering so you get a consistent look, the gap between 35-70 isn't really all that significant in real world terms, and you've got a lot of range to play with there. They're also both nicely sealed while being just a little bit easier to carry around than the f/2.8 equivalents.
The 17-40 and 70-300 L lenses are a step down in quality but they're cheaper and you get a little more long end. There's also an old 28-300 L which is pretty outdated but not really that different in performance from the 24-105 mk I, so if you wish the 24-105 mk I simply had more long-end range, that's worth looking at. Of course there is the 100-400mm but unless you're seriously into wildlife, that's going to be overkill. (And if you were, the 400mm f/5.6 is a much easier lens to "walk around" with.)
... But those really are all a bit much for "walk around", even for longer and more exploratory trips. If your idea of "walk around" means "I need to capture
everything no matter what" then hey, there you go.
If you're more in the latter group and you're doing what more people mean by simply "walk around" then your existing 24-105 is basically as good as it gets. You could spend a little money to switch it for the Sigma 24-105, which is a little sharper, but that's really about it in terms of zoom lenses; everything else which has more range is slower and optically worse, and everything which is faster and/or optically better is more limited and also much heavier and bulkier.
If 24mm isn't wide enough for you and 105mm isn't long enough for you, and you did want to keep bulk down to a minimum, I'd say look for a 20mm prime—there are several around—and a 135mm. Then you're missing out the middle, but if the range is what bothers you then I'm guessing the middle focal lengths aren't too important for you anyway. You could add something like the 40mm STM to fill out that middle range without really adding much weight. But swapping between three primes doesn't really fit the idea of a simple "walk around" solution.
I'd highly recommend you consider, if you're not happy with the 24-105, simply swapping for a basic middle prime. The Tamron 45mm VC, for example, is basically the best all-rounder money can buy at the moment; nearly perfectly 'standard' field of view, excessive weather sealing, and stabilisation. You can stitch a panorama when you want a really wide shot, and how often are you really using the long end of your 24-105, let alone wanting something longer, when you're casually shooting? Working with a single prime isn't for everyone, but it's always something to keep in mind; it's way too easy to think you need to have everything covered, so you load up on gear for every specific purpose and then never really get any pictures because taking everything with you is too much hassle. Sometimes simpler is actually more versatile.
Also, another thing to consider is to ditch Canon. Keep it for your 'real' shooting, by all means, but for "walk around" a lot of people are switching to smaller mirrorless systems and getting great results. Fuji, Sony, and Olympus are dominating the "walk around" market right now, for good reason. (Panasonic are in there too, to a much lesser degree.) They've basically taken over street shooting and event shooting is now pretty 50:50 between the people still lugging SLRs around and those who have switched to smaller systems, and that ratio is only shifting more and more in favour of the mirrorless units.
An extra benefit of picking up one of these systems is they're generally a bit cheaper than their SLR equivalents, so if a small combination gets lost, stolen, or broken in your travels it's not such a big deal, and even a fuller kit is cheaper to insure than an equivalent SLR kit.
Have a hard think about what it is you really
use, what it is you really
need, what you can actually be bothered to carry with you, and the most efficient way to balance that. How often do you find yourself wanting to shoot wider than 24mm and where stitching isn't an option? How often do you find yourself needing to go in more than 105mm and where cropping wouldn't be enough? How much weight and size are you really prepared to put up with? How high of a total equipment value are you prepared to carry?
ahsanford said:
It would appear between all the 18-135 crop, 28-135 / 28-300 FF options that Canon has learned that long standard zooms are easy... providing you don't want wider than 28mm FF. That's apparently where the wheels come off the bus optically.
It's not really to do with the optics taking a dip per se, but more that keeping the optical quality high while going much wider than 28mm/equivalent (with zooms that have a long end; obviously, wide-angle zooms are a whole 'nother story) is very
expensive. It all goes back to the days of analogue where 28mm was a much more commonly-wanted focal length, before it got kind of replaced by 24mm toward the end of the 1980s. Every company (and every factory) is geared up to do 28mm (again, we're talking about for standard zooms here) really well, but anything more is a stretch further and further into unknown territory, as far as zooms go. Obviously 24mm has become quite normal, but even then you're mostly seeing 24-xxx zooms only either as premium ranges or with significant compromises.
Same reason every company keeps making 50mm primes and very few make anything closer to 40. Same way we still have rubbish LCDs on the tops of cameras with <3.2" rear screens, and not nice OLEDs and bigger screens like every other device. It's what the factories happened to start out with, so it just kinda sticks, and deviating from that will always cost a premium and stretch the designers' knowledge. If enough companies did it then these things would eventually become totally common and we could have 24-135 or 20-150 or who knows, but no one company wants to be the one to take the hit by being first.