The advantages of this camera are:
+ A large, low-pass free image sensor with incredibly good sharpness and noise values, identical to that of the more expensive models D5300 / D7100.
+ The 18-105mm kit lens has excellent imaging characteristics and is still small and light. Through this lens of dealing with changing lenses is saved on travel. The focal length range of 18-105mm is almost every situation.
+ An image processing software on board that really brings out from the recordings even without lengthy post on the PC much. Especially Nikon's Active D-Lighting technology for selective contrast enhancement does a good job here. All sample photos are not edited (only smaller).
+ A sophisticated operating concept with a good quick access to key shooting parameters.
+ A very high-quality processing. The camera looks great, is sturdy, feels good and sounds good. After 2 months of continuous testing in dust, heat, cold and humidity, everything is like new.
+ Weight with lens only 880g, very compact dimensions for a DSLR.
The only drawback in my opinion the D3300 towards mirrorless system cameras (Sony, Panasonic) is the right slow autofocus in Live View. But since you already better photographed for good photos for reasons of stability with the viewfinder, this disadvantage does not falling for me so much weight.
The alternatives to this camera for me were the Panasonic Lumix G6 and the Canon 700d. The G6 with 14-140mm would also be useful and even / was smaller, lighter, fell after a detailed test but by a massive Shutter-shock problem of (camera shake by the release, see my review of the G6) and affects less robust. The 700d is certainly also a good camera, but especially with its 18-135mm kit lens is larger and heavier than the D3300. Both are more expensive than the D3300.
Conclusion: The D3300 in the 18-105mm kit is absolutely the perfect choice for a camera, let the produce really good photos on a trip. The price-quality ratio is unbeatable anyway a very strong buy recommendation!
PS: Since I was looking for even long, here's my tip for a camera bag: Lowepro Rezo TLZ 20 In the Camera with lens fits well without losing the advantage of compactness by too large bag.