iphones are fantastic for what they can do - light, convenient, always available... But, of course they have serious drawbacks too - tiny lens and sensor, fixed aperture, slow, short battery life, terrible low light performance...

If you can afford it, I would definitely recommend getting a good camera (I really want to try a Sony RX100 II or III). I can't make specific recommendations, as I've never had a great camera (the best I've got is a Kodak Easyshare z760 I got as a gift), but there are a few things you can do to improve the photos taken by an iphone, if you're willing to work within it's limitations. For example, always stabilize it against something if you can. Try to use it only in well lit scenes. If you must take low light photos (I can't seem to stay away from them myself), you can try an app like Cortex Cam, which will actually take several exposures, align them, and pick the median of every pixel, all automatically. This results in a much cleaner picture, but of course, it can't be used with moving subjects. I can also highly recommend the app HDR3, for scenes with a lot of dynamic range, but it takes a very long time to process a single shot, tying up your phone for a good 30 seconds or more, and it saps juice pretty fast. Makes great shots though, if you can hold the phone still.

A better camera is really the way to go, but don't forget that the humble iphone camera can be a great supplement in addition to it sometimes.