I have a Nikon D3100. I purchased a Sigma DG 70-300mm 1:4-5:6 lens for the zoom. I have had very good luck with it, but don't like having to switch every time I want to "zoom". Is there a lens that would work that would have similar zoom capabilities, but also for "walking around" that wouldn't require me to have to switch ?
There are indeed "superzoom" lenses that can cover from wide to telephoto focal lengths, much the way that a bridge camera's lens can. However, there are tradeoffs.
Getting an 18-200 or 18-300 superzoom lens is generally not going to increase image quality over an 18-55/55-300 or 55-200 "twin kit", and is probably going to cost you about twice as much (e.g., Nikon's 18-200 is in the US$500-$600 range, and the 18-300 is closer to $900, while an 18-55/55-200 combo may cost you (if bought as part of a kit with the camera body) closer to $300.
There are also design compromises to achieve the large zoom range. Most commonly, the performance at the extreme ends of the range are liable to exhibit issues like distortion or chromatic aberration and possibly softness. And at times the distortion may be more complex than can be fixed by simple distortion-correction post-processing software and may require a lens profile to fix (e.g., "wave" distortion, which is a combination of both pincushion and barrel distortion was a hallmark of the Nikkor 18-200 @18mm, iirc) That doesn't mean these are bad lens. They're amazingly good for what they can accomplish. They're extremely convenient lenses from a framing standpoint.
The other drawback of a superzoom lens is that it's liable to be "slow". Both the Nikon 18-300 and 18-200 are f/3.5-6.3, which means they're not liable to be useful for available light shooting, the way a 35/1.8 or 50/1.8 is. If the majority of your walkaround shooting is handheld in the daytime outside in good light, and you're willing to sacrifice some image quality for convenience, then these lenses can be terrific. They are a very popular choice for travel photography when you need to travel light.
Also, be aware that the 18-200 and 18-300 are DX (crop) lenses. If you choose to move up to FX (full-frame), you'll have to swap for the (~US$1k) 28-300.
But, if this is your first system camera, you may also want to consider whether your reluctance to change lenses stems from the unfamiliarity of the task. It's always awkward and slow the first time you learn to do something. Over time, you'll get faster and defter at it, and it can seem much more natural to change lenses. A system camera derives its versatility from its ability to use the rest of the system. Restricting yourself to a single lens removes a lot of versatility from your camera.
And if you find that a dSLR may be more camera than you wanted, but you love the large sensor, there are, these days, large-sensored compact cameras with fixed lenses.